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

on the generation of skeletons from discrete euclidean distance maps the skeleton is an important representation for shape analysis a common approach for generating discrete skeletons takes three steps 1 computing the distance map 2 detecting maximal disks from the distance map and 3 linking the centers of maximal disks cmds into a connected skeleton algorithms using approximate distance metrics are abundant and their theory has been well established however the resulting skeletons may be inaccurate and sensitive to rotation in this paper we study methods for generating skeletons based on the exact euclidean metric we first show that no previous algorithms identify the exact set of discrete maximal disks under the euclidean metric we then propose new algorithms and show that they are correct to link cmds into connected skeletons we examine two prevalent approaches connected thinning and steepest ascent we point out that the connected thinning approach does not work properly for euclidean distance maps only the steepest ascent algorithm produces skeletons that are truly medially placed the resulting skeletons have all the desirable properties they have the same simple connectivity as the figure they are well centered they are insensitive to rotation and they allow exact reconstruction the effectiveness of our algorithms is demonstrated with numerous examples

very weak generalized and strong solutions to the stokes system in the half space abstract in this paper we study the stokes system in the half space r n with n 2 we give existence and uniqueness results in weighted sobolev spaces after the central case of the generalized solutions we are interested in strong solutions and symmetrically in very weak solutions by means of a duality argument

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 delta medial axis in this paper we present the delta medial axis dma a quasi linear algorithmic solution addressing several of the main concerns of discrete medial axes ma computation first its sensitivity to small shape perturbations is counterbalanced by a single parameter delta used in a pruning strategy that implicitly takes into account the local topology of the boundary second the discrete nature of images is addressed by approximating the original ma definition in continuous space third to allow real time performances a set of algorithmic optimizations is proposed we compare our approach both qualitatively and quantitatively to recent state of the art solutions and show that the dma presents an excellent choice for a wide range of applications finally to allow fast and efficient use of our algorithm we propose the complete pseudo code highlightsthe delta medial axis a fast and robust skeletonization algorithm is presented it includes a pruning parameter which considers the local topology of the boundary to allow real time performances optimizations are introduced with complete pseudo code a complete comparative study with four recent state of the art algorithms is proposed

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

on the noether lefschetz theorem and some remarks on codimension two cycles here of general moduli means that there is a countable union v of subvarieties of the space pn of surfaces of degree d in p3 such that the statement pie s z holds for s p n v noether it would seem stated this theorem but never completely proved it instead he gave a plausibility argument based on the following construction 1 let g be the hilbert scheme of curves of degree n and genus 9 in p3 l gr3 d l ip n the space of surfaces of degree d in p3 and zc t the incidence correspondence s o a c s c z s

tate s conjecture for k3 surfaces of finite height this paper extends the proof 16 of the tate conjecture for ordinary k3 surfaces over a finite field to the more general case of all k3 s of finite height as in 16 our method is to find a lifting of the k3 to characteristic zero with sufficiently many hodge cycles in the ordinary case the so called canonical lifting of deligne and illusie 7 did the job and a study of the galois action on p adic etale cohomology revealed the hodge cycles here we use more general quasi canonical liftings and the action of the crystalline weil group on

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

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

a1 curves on log k3 surfaces abstract in this paper we study a 1 curves on log k3 surfaces we classify all genuine log k3 surfaces of type ii which admit countably infinite a 1 curves

uniruledness of strata of holomorphic differentials in small genus abstract we address the question concerning the birational geometry of the strata of holomorphic and quadratic differentials we show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on k3 and del pezzo surfaces respectively restricting to genus 3 g 6 we construct projective bundles over a rational varieties that dominate the holomorphic strata with length at most g 1 hence showing in addition that these strata are unirational

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

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

a level set method for anisotropic geometric diffusion in 3d image processing a new morphological multiscale method in three dimensional 3d image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems its aim is to smooth the level sets of a 3d image while simultaneously preserving geometric features such as edges and corners on the level sets this is obtained by an anisotropic curvature evolution where time serves as the multiscale parameter thereby the diffusion tensor depends on a regularized shape operator of the evolving level sets as one suitable regularization local l2 projection onto quadratic polynomials is considered the method is compared to a related parametric surface approach and a geometric interpretation of the evolution and its invariance properties is given a spatial finite element discretization on hexahedral meshes and a semi implicit regularized backward euler discretization in time are the building blocks of the easy to code algorithm different a

nonhomogeneous biharmonic problem in the half space l p theory and generalized solutions abstract in this paper we study the biharmonic equation in the half space r n with n 2 we prove in l p theory with 1 p existence and uniqueness results we consider data and give solutions which live in weighted sobolev spaces

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

hierarchic voronoi skeletons abstract robust and time efficient skeletonization of a planar shape which is connectivity preserving and based on euclidean metrics can be achieved by first regularizing the voronoi diagram vd of a shape s boundary points i e by removal of noise sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents each component of the vd is attributed with a measure of prominence which exhibits the expected invariance under geometric transformations and noise the second processing step a hierarchic clustering of skeleton branches leads to a multiresolution representation of the skeleton termed skeleton pyramid

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

density of rational curves on k3 surfaces using the dynamics of self rational maps of elliptic k3 surfaces together with deformation theory we prove that the union of rational curves is dense on a very general k3 surface and that the union of elliptic curves is dense in the 1st jet space of a very general k3 surface both in the strong topology

noether lefschetz theory and the yau zaslow conjecture the yau zaslow conjecture predicts the genus 0 curve counts of k3 surfaces in terms of the dedekindfunction the classical intersection theory of curves in the moduli of k3 surfaces with noether lefschetz divisors is related to 3 fold gromov witten invariants via the k3 curve counts results by borcherds and kudla millson determine these classical intersections in terms of vector valued modular forms proven mirror transformations can often be used to calculate the 3 fold invariants which arise via a detailed study of the stu model determining special curves in the moduli of k3 surfaces we prove the yau zaslow conjecture for all curve classes on k3 surfaces two modular form identities are required the first the klemm lerche mayr identity relating hypergeometric series to modular forms after mirror trans formation is proven here the second the harvey moore identity is proven by d zagier and presented in the paper

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

kontsevich spaces of rational curves on fano hypersurfaces we investigate the spaces of rational curves on a general hypersurface in particular we show that for a general degree d hypersurface in pn with n d 2 the space m0 0 x e of degree e kontsevich stable maps from a rational curve to x is an irreducible local complete intersection stack of dimension e n d 1 n 4 this resolves all but one case of a conjecture of coskun harris and starr

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

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

a competition flow method for computing medial axis transform abstract medial axis computation mac has many applications in computer aided design computer graphics automated mesh generation solid modeling cnc tool path generation robotic motion planning bioinformatics and shape analysis there are three key issues that need to be further addressed on mac of a nurbs non uniform rational b spline curve boundary namely 1 computation of regular medial axis points 2 efficient detection of the existence of a branch point where two branches intersect and 3 convergence and correctness on computing the position of a branch point this paper presents a competition flow method for medial axis computation of a planar simply connected nurbs boundary different from previous methods which trace a voronoi diagram tree vdt in depth first order from a terminal point the competition flow method cfm traces the corresponding tree in breadth first order it has three main contributions firstly it utilizes an optimized method based on previous state of art algorithms for computing regular medial axis points which can achieve a higher computational efficiency secondly it implements a divide and conquer method in a natural way by proposing a simple tree technique in which a vdt is divided into several simple tree structures of level l l 0 1 for competitive medial axis computation finally by using the competition flow method possible places where branch points are located are intuitively and efficiently detected and bounded with high precision which ensures the convergence and the correctness of the computation of the position of a branch point and also ensures the correctness of the topological structure of the medial axis tree numerical examples show that the new method can achieve a better performance compared with several existing methods

constructing rational curves on k3 surfaces we develop a mixed characteristic version of the morimukai technique for producing rational curves on k3 surfaces we reduce modulo p produce rational curves on the resulting k3 surface over a finite field and lift to characteristic zero as an application we prove that all complex k3 surfaces with picard group generated by a class of degree two have an infinite number of rational curves

moduli of nodal curves on k3 surfaces abstract we consider modular properties of nodal curves on general k3 surfaces let k p be the moduli space of primitively polarized k3 surfaces s l of genus p 3 and v p m k p be the universal severi variety of nodal irreducible curves in m l on s l k p we find conditions on p m for the existence of an irreducible component v of v p m on which the moduli map v m g with g m 2 p 1 1 has generically maximal rank differential our results which for any p leave only finitely many cases unsolved and are optimal for m 5 except for very low values of p are summarized in theorem 1 1 in the introduction

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

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

skeleton pruning by contour partitioning with discrete curve evolution in this paper we introduce a new skeleton pruning method based on contour partitioning any contour partition can be used but the partitions obtained by discrete curve evolution dce yield excellent results the theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable even in the presence of significant noise and shape variations and have the same topology as the original skeletons in particular we have proven that the proposed approach never produces spurious branches which are common when using the known skeleton pruning methods moreover the proposed pruning method does not displace the skeleton points consequently all skeleton points are centers of maximal disks again many existing methods displace skeleton points in order to produces pruned skeletons

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

modular properties of nodal curves on k3 surfaces in this article we are going to address the following issues 1 the first is a rigidity property for pairs s c consisting of a general projective k3 surface s and a curve c obtained as the normalization of a nodal hyperplane section hat c hookrightarrow s we prove that a non trivial deformation of a pair s c induces a non trivial deformation of c 2 the second question concerns the wahl map of curves c obtained as above we prove that the wahl map of the normalization of a nodal curve contained in a general projective k3 surface is non surjective in both cases we impose upper bounds on the number of nodes of hat c

on universal severi varieties of low genus k3 surfaces we prove the irreducibility of universal severi varieties parametrizing irreducible reduced nodal hyperplane sections of primitive k3 surfaces of genus g with 3 g 11 g 10

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

euclidean skeletons of digital image and volume data in linear time by the integer medial axis transform a general algorithm for computing euclidean skeletons of 2d and 3d data sets in linear time is presented these skeletons are defined in terms of a new concept called the integer medial axis ima transform we prove a number of fundamental properties of the ima skeleton and compare these with properties of the cmd centers of maximal disks skeleton several pruning methods for ima skeletons are introduced constant linear and square root pruning and their properties studied the algorithm for computing the ima skeleton is based upon the feature transform using a modification of a linear time algorithm for euclidean distance transforms the skeletonization algorithm has a time complexity which is linear in the number of input points and can be easily parallelized we present experimental results for several data sets looking at skeleton quality memory usage and computation time both for 2d images and 3d volumes

rational curves on k3 surfaces we show that projective k3 surfaces with odd picard rank contain infinitely many rational curves our proof extends the bogomolov hassett tschinkel approach i e uses moduli spaces of stable maps and reduction to positive characteristic

lines on quartic surfaces we show that the maximal number of real lines in a real nonsingular spatial quartic surface is 64 respectively 56 we also give a complete projective classification of all quartics containing more than 52 lines all such quartics are projectively rigid any value not exceeding 52 can appear as the number of lines of an appropriate quartic

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed