chow groups of projective varieties of very small degree see 12 5 and the references given there these facts together with various conjectures on the cohomology and chow groups of algebraic varieties suggest that the chow groups of x might satisfy chl x q chl pk q q for l 1 compare with remark 5 6 and corollary 5 7 this is explicitly formulated by v srinivas and k paranjape in 16 conjecture 1 8 the chain of reasoning goes roughly as follows suppose x is smooth one expects a good filtration 0 f j 1 f j f 0 ch x x q whose graded pieces f f l 1 are controlled by h2j l x x see 10 according to grothendieck s generalized conjecture 8 the groups h x should be generated by the image under the gysin morphism of the homology of a codimension subset together with the classes coming from p applying this to the diagonal in x x should then force the triviality of the chow groups in the desired range for zero cycles the conjecture follows from roitman s theorem see 17 and 18

semi crossed products of c algebras abstract given a c algebra u and endomorphim there is an associated nonselfadjoint operator algebra z x u called the semi crossed product of u with if is an automorphim z x u can be identified with a subalgebra of the c crossed product z x u if u is commutative and is an automorphim satisfying certain conditions z x u is an operator algebra of the type studied by arveson and josephson suppose s is a locally compact hausdorff space s s is a continuous and proper map and is the endomorphim of u c0 s given by necessary and sufficient conditions on the map are given to insure that the semi crossed product z x c0 s is i semiprime ii semisimple ii strongly semisimple

a new fast physical optics for smooth surfaces by means of a numerical theory of diffraction a new technique to compute the physical optics po integral is presented the technique consists of a blind code that computes the different contributions stationary phase points end points etc numerically this technique is based on a decomposition of the surface into small triangles and a fast evaluation of each triangle by means of a deformation of the integration path in the complex plane this algorithm permits a fast and accurate evaluation of the po integral for smooth large surfaces the cpu time is almost independent of frequency

computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method in this work the computation of physical optics po type integral with the integrand of quadratic phase and amplitude is studied first we apply the numerical steepest descent path nsdp method to calculate the highly oscillatory po integral on the triangular patch then we rigorously extend the proposed nsdp method to analyze the po integral on polygonal domains furthermore the contributions of critical points on polygonal domains including the stationary phase point resonance and vertex points are comprehensively studied in terms of the nsdp method compared to the traditional high frequency asymptotic hfa method when the wave frequency is not very high but in the high frequency regime the nsdp method has improved the po integral accuracy by one to two digits meanwhile the computational cost by using the proposed nsdp method is independent of the wave frequency

operator algebras and the conjugacy of transformations abstract a family of algebras is associated with each continuous map on a compact hausdorff space these algebras are called conjugacy algebras it is shown that two continuous maps are conjugate if and only if some conjugacy algebra of one is isomorphic to some conjugacy for the other numerous examples of conjugacy algebras are provided

groupe de chow de codimension deux des varietes definies sur un corps de nombres un theoreme de finitude pour la torsion letx be a smooth projective variety defined over a number field and let ch2 x denote the chow group of codimension two cycles modulo rational equivalence we show that if the cohomology grouph2 x ox vanishes then the torsion subgroup of ch2 x is a finite group this result covers all previous results in this direction the hypothesish2 x ox 0 is used to lift line bundles

the arithmetic of zero cycles on surfaces with geometric genus and irregularity zero let x be a smooth projective geometrically irreducible surface over a perfect field f throughout this paper it will be assumed that the geometric genus pg and the irregularity q of x both vanish denote the separable closure of f by f let x x be the surface obtained from x by base extension it will also be assumed that the group ao x of rational equivalence classes of zero cycles of degree zero on x vanishes this is a technical hypothesis which could presumably be eliminated at the expense of working with ker ao x ao x for want of a better name and for ease in stating various results any surface which satisfies these three hypotheses will be called a pseudo rational surface bloch 2 has conjectured that the vanishing of ao x should follow from the assumption that po q 0 this was proven by bloch kas and lieberman 5 for all such surfaces which are not of general type i e which have kodaira dimension less than 2 it has also been proven for particular surfaces of general type by inose and mizukami 23 barlow 1 and keum 25 consequently the class of pseudo rational surfaces includes rational surfaces enriques surfaces elliptic surfaces with q 0 the classical godeaux surface burniat inoue surfaces campedelti surfaces and the surfaces of barlow and of keum this paper will study ao x for pseudo rational surfaces defined over fields of number theoretic interest bloch 4 introduced k theoretic techniques into the study of zero cycles on rational surfaces his work was extended 7 12 15 27 28 32 36 to achieve a thorough understanding of such cycles colliot th616ne and raskind 10 developed this machinery further to study codimension two cycles on any variety the author 14 applied these techniques to enriques surfaces raskind 30 used them to study zero cycles on pseudo rational surfaces one of the main results of this paper is a new proof of the following theorem of raskind 31

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

semicrossed products of operator algebras and their c envelopes abstract let a be a unital operator algebra and let be an automorphism of a that extends to a automorphism of its c envelope c env a we introduce the isometric semicrossed product a is z and we show that c env a is z c env a z in contrast the c envelope of the familiar contractive semicrossed product a z may not equal c env a z our main tool for calculating c envelopes for semicrossed products is a new concept the relative semicrossed product of an operator algebra by an endomorphism as an application of our theory we show that if t x is the tensor algebra of a c correspondence x a and is a extendible automorphism of t x that fixes the diagonal elementwise then the contractive semicrossed product satisfies c env t x z o x z where o x denotes the cuntz pimsner algebra of x a this extends the main result of davidson and katsoulis 2010 6

examples of smash nilpotent cycles on rationally connected varieties abstract voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety we prove this conjecture holds for uniruled 3 folds 4 folds whose mrcc quotient has dimension 2 and for smooth complete intersections with very small degree

motives and filtrations on chow groups in this paper sequential to sa we discuss a philosophy of bloch and beilinson concerning filtrations on chow groups of algebraic vareties which provides us with a good understanding on the structure of at least certain portions of chow groups let k be a fixed ground field and let c be the category of smooth projective schemes over k with a fixed suitable weil cohomology theory cf notations x in mathcal c rightsquigarrow h x mathop oplus limits i in z h i x

rost nilpotence and higher unramified cohomology abstract we develop an approach to proving the rost nilpotence principle involving higher unramified cohomology along with a decomposition of the diagonal technique we use this to prove the principle for certain threefolds over a perfect field

the rost nilpotence theorem for geometrically rational surfaces we show that the rost nilpotence theorem is true for geometrically rational surfaces over fields of characteristic zero

positivity of the diagonal abstract we study how the geometry of a projective variety x is reflected in the positivity properties of the diagonal x considered as a cycle on x x we analyze when the diagonal is big when it is nef and when it is rigid in each case we give several implications for the geometric properties of x for example when the cohomology class of x is big we prove that the hodge groups h k 0 x vanish for k 0 we also classify varieties of low dimension where the diagonal is nef and big

complex multiplication cycles and a conjecture of beilinson and bloch a generalization of the conjecture of birch and swinnerton dyer is investigated using complex multiplication cycles on a particular kuga fiber variety a weak finiteness result consistent with the conjecture is proved the image of complex multiplication cycles under the abel jacobi map is computed explicitly the results provide numerical evidence supporting the conjecture they also give evidence for a relationship between complex multiplication cycles and a modular form of weight 5 2 and raise questions for further investigation

2 cycles sur les hypersurfaces cubiques de dimension 5 we study 2 cycles of a smooth cubic hypersurface of dimension 5 we show that the griffiths group of 2 cycles is trivial and the abel jacobi map induces an isomorphism between the chow group of algebraically trivial 2 cycles and the intermediate jacobian

a hyper kahler compactification of the intermediate jacobian fibration associated with a cubic 4 fold let x be a general cubic fourfold it was observed by donagi and markman that the relative intermediate jacobian fibration j u with u p5 x associated to the smooth hyperplane sections of x carries a natural holomorphic symplectic form making the fibration lagrangian in this paper we obtain a smooth projective compactification j of j with the property that the holomorphic symplectic form on j extends to a holomorphic symplectic form on j in particular j is a 10 dimensional compact hyper kahler manifold which we show to be deformation equivalent to the exceptional example of o grady this proves a conjecture by markushevich

a pencil of enriques surfaces with non algebraic integral hodge classes we prove that there exists a pencil of enriques surfaces defined over mathbb q with non algebraic integral hodge classes of non torsion type this gives the first example of a threefold with the trivial chow group of zero cycles on which the integral hodge conjecture fails as an application we construct a fourfold which gives the negative answer to a classical question of murre on the universality of the abel jacobi maps in codimension three

c envelopes of semicrossed products by lattice ordered abelian semigroups abstract a semicrossed product is a non selfadjoint operator algebra encoding the action of a semigroup on an operator or c algebra we prove that when the positive cone of a discrete lattice ordered abelian group acts on a c algebra the c envelope of the associated semicrossed product is a full corner of a crossed product by the whole group by constructing a c cover that itself is a full corner of a crossed product and computing the shilov ideal we obtain an explicit description of the c envelope this generalizes a result of davidson fuller and kakariadis from z n to the class of all discrete lattice ordered abelian groups

efficient evaluation of highly oscillatory acoustic scattering surface integrals we consider the approximation of some highly oscillatory weakly singular surface integrals arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three dimensional convex obstacles described globally in spherical coordinates as the frequency of the incident wave increases the performance of standard quadrature schemes deteriorates naive application of asymptotic schemes also fails due to the weak singularity we propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system for the case of a spherical scatterer we demonstrate via error analysis and numerical results that provided the observation point is sufficiently far from the shadow boundary a high level of accuracy can be achieved with a minimal computational cost

efficient algorithm for the evaluation of the physical optics scattering by nurbs surfaces with relatively general boundary condition an adaptive integration algorithm is presented for the computation of the physical optics po electric and magnetic field scattered by electrically large objects modeled by non uniform rational b splines nurbs the algorithm is the customization of a more general purpose result that has been recently published by using a unique formulation both impenetrable e g impedance surfaces coated conductors as well as transparent thin sheet materials e g thin dielectric panels or frequency selective surfaces are treated via their fresnel reflection and transmission coefficients the po radiation integral is evaluated over the nurbs parametric domain since most of the computer aided geometric design cagd tools are based on nurbs the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description with no need of generating new geometrical models furthermore the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard nyquist based sampling integration algorithms such reduction of the sampling points is achieved by resorting to high frequency technique concepts and allows a significant reduction of the cpu computational burden therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real life electrically large objects

the hodge conjecture for a certain class of singular varieties in j there is stated a version of the hodge conjecture for complex singular varieties reduced separated algebraic schemes over c generalizing the popular version of the conjecture a statement of the general hodge conjecture for the singular case extending the amended version by grothendieck is given in l2 using the techniques in j the statement is this let z be a reduced separated algebraic scheme over c the lowest weight part w i hi z q of the borelmoore homology hi z q defines a hodge structure of weight i recall the filtration by niveau given by

rost nilpotence and etale motivic cohomology abstract a smooth projective scheme x over a field k is said to satisfy the rost nilpotence principle if any endomorphism of x in the category of chow motives that vanishes on an extension of the base field k is nilpotent we show that an etale motivic analogue of the rost nilpotence principle holds for all smooth projective schemes over a perfect field this provides a new approach to the question of rost nilpotence and allows us to obtain an elegant proof of rost nilpotence for surfaces as well as for birationally ruled threefolds over a field of characteristic 0

class field theory for a product of curves over a local field we prove that the kernel of the reciprocity map for a product of curves over a p adic field with split semi stable reduction is divisible we also consider the k1 of a product of curves over a number field

rational curves on complete intersections in positive characteristic abstract we study properties of rational curves on complete intersections in positive characteristic it has long been known that in characteristic 0 smooth calabi yau and general type varieties are not uniruled in positive characteristic however there are well known counterexamples to this statement we will show that nevertheless a general calabi yau or general type complete intersection in projective space is not uniruled we will also show that the space of complete intersections of degree d 1 d k containing a rational curve has codimension at least i 1 k d i 2 n 2 and give similar results for hypersurfaces containing higher genus curves

on the modified theory of physical optics basic features of the modified theory of physical optics mtpo are discussed on the example of scattering at perfectly reflecting half planes and wedges it is shown that violations of the geometrical optics go introduced in this technique result in the mtpo solutions which do not satisfy the helmholtz equation they are incorrect at a finite distance from a scattering object however it can be considered as sort of approximations for the field at a large distance from an edge and away from the go boundaries

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

2 cycles on higher fano hypersurfaces let x d be a smooth hypersurface of degree d in mathbb p mathbb c n suppose that the fano variety mathrm f x d of lines of x d is smooth we prove that the griffiths group mathrm griff 1 mathrm f mathrm x d of mathrm f x d is trivial if the hypersurface mathrm x d is of 2 fano type as a result we give a positive answer to a question of professor voisin about the first griffiths groups of fano varieties in some cases base on this result we prove that mathrm ch 2 mathrm x d mathbb z for a smooth 3 fano hypersurface mathrm x d subseteq mathbb p n mathbb c with smooth fano variety of lines

motifs l functions and the k cohomology of rational surfaces over finite fields let x be a smooth projective variety over a field let f denote the zariski sheaf associated to the presheaf u kj f u cv of quillen k groups the collection of zariski cohomology groups h x fj will be referred to as the k cohomology of x the groups contain a great deal of information about the geometry of x for example bloch s formula 11 says that hi x is isomorphic to the group ctt x of codimension i cycles on x modulo rational equivalence in this paper the k cohomology of a rational surface over a finite field will be calculated up to p torsion where p is the characteristic recall that a surface x over a field f is called rational if z x is birational with i 3 over the algebraic closure f motifs play a central role in the computation the idea that motifs could be used effectively to study the k theory of varieties over finite fields is due to soulr whose paper 15 is a fertile source of inspiration he introduced the k cohomology of motifs and proved several important finiteness results in particular he showed for a wide class of varieties including rational surfaces that ki x is torsion for j 0 a second source of ideas is the fundamental work of merkurjev and suslin i 8 especially as applied in 4 to codimension two cycles and in 17 to the k2 cohomology of rational surfaces the paper is organized as follows the first section contains a brief review of the theory of motifs from the motivic point of view all the relevant data about a rational surface is contained in the action of the galois group on pic x this action is a continuous finite dimensional integral galois representation the second section contains a computation of the prime to p k theory of such representations when f is finite in the final section the orders of the k cohomology groups are related to the values at integer points of the l functions associated to x let f q ig and let l be a prime different from p let 4j denote the endomorphism of the ale c0homology group hj x r which is induced by the q power frobenius define p t det 1 and lj s pj q also if a b write a b to mean that a b is a power of p

lawson homology for varieties with small chow groups and the induced filtration on the griffiths groups these groups form an intriguing set of invariants despite the vast literature on this subject the groups have been calculated only in very few cases such as for the projective spaces one of the goals of this note is to understand these invariants in case the variety has few cycles in the sense that rational and homological equivalence coincide for all m cycles up to a certain rank m s actually the results only deal with that part of lawson homology that is not visible in ordinary homology in that it is in the kernel of the cycle class maps cm k 2m lmhk 2m x hk 2m x

efficient evaluation of the physical optics integrals for conducting surfaces using the uniform stationary phase method the computational time to evaluate the physical optics po expression by numerical integration increases rapidly with the increase of electrical size of scattering surfaces however the computational time of po integrals for electrically large object can be greatly reduced by using the stationary phase method which is independent of the wavenumber for this method the theory and numerical implementations for isolated critical points have been well developed however for cases of nearby critical points there are still a few issues to be considered especially in numerical implementations in this paper we mainly study the numerical implementations for several most common cases of nearby critical points in particular the cases of two nearby inner stationary phase points and complex inner stationary phase points are discussed in more details such cases occur frequently when the scattering surface includes convex concave parts but the numerical implementations to such cases have not been reported to our knowledge the difficulty lies in how to identify whether two inner stationary points and complex inner stationary points on the surfaces with arbitrary shapes are close to each other or not a strategy is designed to solve this difficulty by validation in some typical examples we find that the stationary phase method is robust enough to evaluate the po integrals accurately finally some interesting phenomena observed in numerical validations are interpreted

tamagawa numbers of diagonal cubic surfaces numerical evidence a refined version of manin sconjecture aboutthe asymptotics of points of bounded height on fano varieties has been developped by batyrev and the authors we test numerically this refined conjecture for some diagonal cubic surfaces

non trivial elements in the abel jacobi kernels of higher dimensional varieties abstract the purpose of this paper is to construct non trivial elements in the abel jacobi kernels in any codimension by specializing correspondences with non trivial hodge theoretical invariants at points with different transcendence degrees over a subfield in c

on the fibration method for zero cycles and rational points conjectures on the existence of zero cycles on arbitrary smooth projective varieties over number elds were proposed by colliot th el ene sansuc kato and saito in the 1980 s we prove that these conjectures are compatible with brations for brations into rationally connected varieties over a curve in particular they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers we prove the analogous result for rational points conditionally on a conjecture on locally split values of polynomials which a recent work of matthiesen establishes in the case of linear polynomials over the rationals

an alternative treatment of saddle stationary phase points in physical optics for smooth surfaces in a recent paper on computing the physical optics po integral with a saddle stationary phase point spp by numerical steepest descend method nsdm f vico bondia a new fast physical optics for smooth surfaces by means of a numerical theory of diffraction ieee trans antennas propag vol 58 no 3 pp 773 789 mar 2010 a one dimensional integral was obtained on the path of which there existed higher order up to third poles to avoid tackling the singular integral the abel s summation technique was used to solve the problem ingeniously however it has been shown in some literatures that the integral would be divergent if there were even order poles on the path of integral superficially the integral in f vico bondia s paper does not obey this law and the main aim of the communication is to clear this contradiction we show rigorously that higher order poles have no contributions to the final result to acquire a general law we further consider arbitrary polynomials of higher degrees for the po integral in which the orders of poles can be arbitrary number in such a general case we still show that all higher order poles have no contributions and thus solve the contradiction satisfactorily numerical examples are presented to validate the new derivations and illustrate the accuracy and efficiency of nsdm

isomorphisms between topological conjugacy algebras a family of algebras which we call topological conjugacy algebras is associated with each proper continuous map on a locally compact hausdorff space assume that i xi xi is a continuous proper map on a locally compact hausdorff space xi for i 1 2 we show that the dynamical systems x1 1 and x2 2 are conjugate if and only if some topological conjugacy algebra of x1 1 is isomorphic as an algebra to some topological conjugacy algebra of x2 2 this implies as a corollary the complete classification of the semicrossed products c0 x z which was previously considered by arveson and josephson 3 peters 19 hadwin and hoover 8 and power 21 we also obtain a complete classification of all semicrossed products of the form a d z where a d denotes the disc algebra and d d a continuous map which is analytic on the interior in this case a surprising dichotomy appears in the classification scheme which depends on the fixed point set of we also classify more general semicrossed products of uniform algebras

decomposition of small diagonals and chow rings of hypersurfaces and calabi yau complete intersections abstract on the one hand for a general calabi yau complete intersection x we establish a decomposition up to rational equivalence of the small diagonal in x x x from which we deduce that any decomposable 0 cycle of degree 0 is in fact rationally equivalent to 0 up to torsion on the other hand we find a similar decomposition of the smallest diagonal in a higher power of a hypersurface which provides us an analogous result on the multiplicative structure of its chow ring

permutation modules and chow motives of geometrically rational surfaces abstract we prove that the chow motive with integral coefficient of a geometrically rational surfaces s over a perfect field k is zero dimensional if and only if the picard group of k k s where k is an algebraic closure of k is a direct summand of a gal k k permutation module and s possesses a zero cycle of degree one as shown by colliot thelene in a letter to the author which we have reproduced in the appendix this is in turn equivalent to s having a zero cycle of degree 1 and ch 0 k s k s being torsion free

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

the jacobson radical for analytic crossed products we characterise the jacobson radical of an analytic crossed product c0 x z answering a question first raised by arveson and josephson in 1969 in fact we characterise the jacobson radical of analytic crossed products c0 x zd this consists of all elements whose fourier coefficients vanish on the recurrent points of the dynamical system and the first one is zero the multidimensional version requires a variation of the notion of recurrence taking into account the various degrees of freedom

evaluation of physical optics integrals from b spline surfaces by means of a fast locating algorithm of stationary points a novel modeling method based on the parametric domain decomposition is proposed for the b spline surfaces this method combines the advantages of conventional b spline and bezier surfaces moreover a fast algorithm based on the new modeling method is presented to locate the stationary points including inner and boundary stationary points of physical optics po integrals from targets modeled with double quadratic b spline surfaces in this algorithm the locating problem is reduced to a numerical or analytical solution no approximation is involved in the proposed modeling method and locating algorithm the stationary phase method by means of the fast locating algorithm is employed to evaluate po integrals the cpu time is independent of the incident frequency and physical dimension of scattered surfaces the accuracy and performance of the presented methods are validated by comparing them with those of the brute force method

levels of function fields of surfaces over number fields we study the level of nonformally real function fields of surfaces over number fields and show that it is at most 4 for a large class of surfaces

on the unramified cohomology of certain quotient varieties in this note we consider unramified cohomology with mathbb z 2 coefficients for some degree two quotient varieties and describe a method that allows one to prove the non vanishing of these groups under certain conditions we apply this method to prove a non vanishing statement in the case of kummer varieties combining this with work of colliot thelene and voisin we obtain a new type of three dimensional counterexample to the integral hodge conjecture

potential density of rational points on the variety of lines of a cubic fourfold we prove the potential density of rational points on the variety of lines of a sufficiently general cubic fourfold defined over a number field where sufficiently general means that a condition of terasoma type is satisfied these varieties have trivial canonical bundle and have geometric picard number equal to one

bloch s conjecture for catanese and barlow surfaces catanese surfaces are regular surfaces of general type with pg 0 they specialize to double covers of barlow surfaces we prove that the ch0 group of a catanese surface is equal to z which implies the same result for the barlow surfaces

rationally connected varieties over local fields let x be a proper variety defined over a field k following ma we say that two points x x x k are r equivalent if they can be connected by a chain of rational curves defined over k cf 4 1 in essence two points are r equivalent if they are obviously rationally equivalent several authors have proved finiteness results over local and global fields cubic hypersurfaces ma sd linear algebraic groups ct sa vo1 gi vo2 rational surfaces ct co ct1 ct sk1 quadric bundles and intersections of two quadrics ct sa sd pa su r equivalence is only interesting if there are plenty of rational curves on x at least over k such varieties have been studied in the series of papers komi mo1 ko mi mo3 see also ko1 there are many a priori different ways of defining what plenty of rational curves should mean fortunately many of these turn out to be equivalent and this leads to the notion of rationally connected varieties see ko mi mo2 ko1 iv 3 ko2 4 1 2

the numerical steepest descent path method for calculating physical optics integrals on smooth conducting quadratic surfaces in this paper we use the numerical steepest descent path nsdp method to analyze the highly oscillatory physical optics po integral on smooth conducting parabolic surfaces including both monostatic and bistatic cases quadratic variations of the amplitude and phase functions are used to approximate the integrand of po integral then the surface po integral is reduced into several highly oscillatory line integrals by invoking the nsdp method these highly oscillatory po line integrals are defined on the corresponding nsdps furthermore the critical point contributions for the po integral are exactly extracted and represented based on the nsdps the proposed nsdp method for calculating the po integral on the smooth conducting surfaces is frequency independent and error controllable compared with the traditional asymptotic expansion approach the nsdp method significantly improves the po integral accuracy by around two digits when the working wave frequencies are not extremely large numerical results are given to validate the nsdp method

on the action of symplectic automorphisms on the mathrm ch _0 groups of some hyper kahler fourfolds we prove that for any polarized symplectic automorphism of the fano variety of lines of a smooth cubic fourfold equipped with the plucker polarization the induced action on the chow group of 0 cycles is identity as predicted by bloch beilinson conjecture we also prove the same result for the chow group of homologically trivial 2 cycles up to torsion

some results on green s higher abel jacobi map this paper is devoted to the study of the flrst higher abel jacobi invariant deflned by m green in 4 for zero cycles on a surface green s work is a very original attempt to understand at least over the graded pieces of the conjecturally deflned flltration on chow groups ch p x f 0 ch p x ae f 1 ch p x c h p x hom ae ae f p 1 ch p x 0

rationally connected varieties over finite fields let x be a geometrically rational or more generally separably rationally connected variety over a finite field k we prove that if k is large enough then x contains many rational curves defined over k as a consequence we prove that r equivalence is trivial on x if k is large enough these results imply the following conjecture of j l colliot thelene let y be a rationally connected variety over a number field f for a prime p let y p denote the corresponding variety over the local field f p then for almost all primes p the chow group of 0 cycles on y p is trivial and r equivalence is trivial on y p

semicrossed products of simple c algebras let mathcal a alpha and mathcal b beta be c dynamical systems and assume that mathcal a is a separable simple c algebra and that and are automorphisms then the semicrossed products mathcal a times alpha mathbb z and mathcal b times beta mathbb z are isometrically isomorphic if and only if the dynamical systems mathcal a alpha and mathcal b beta are outer conjugate

calculation of physical optics integrals over nurbs surface using a delaminating quadrature method physical optics po is a widely used radar cross section rcs estimation approach for electrically large scaled objects and it is finally reduced to the calculation of highly oscillatory integrals in this paper the po integrals over non uniform rational b spline nurbs surfaces is proposed to be calculated with a delaminating quadrature method the method has the merits of being very stable accurate and fast and its computation cost does not increase with frequency moreover in order to keep these good properties for po integrals involving critical points stationary phase point resonant point a scheme of integral subdividing is proposed and new approaches for locating the critical points are also presented numerical examples of flat surface cylindrical surface and spherical surface well show the advantages of the new method