global smoothing of calabi yau threefolds yoshinori namikawa i j h m steenbrink 2 i department of mathematics sophia university kioi cho tokyo 102 japan 2 mathematical institute university of nijmegen toernooiveld 6525 ed nijmegen the netherlands oblatum 10 x 1994 13 vi 1995 introduction friedman fr has studied the relationship between local and global deforma tions of a threefold z with isolated hypersurface singularities which admits small resolutions one of his main results is as follows let z be a moishezon threefold with only ordinary double points pl p assume that the canon ical line bundle

on the pluricanonical maps of varieties of intermediate kodaira dimension in this paper we will prove a uniformity result for the iitaka fibration f x rightarrow y provided that the generic fiber has a good minimal model and the prokhorov shokurov conjecture holds in particular the result holds if the variation of f is zero or kappa x text dim x 1

kodaira dimension of irregular varieties let f x y be an algebraic fiber space with general fiber f if y is of maximal albanese dimension we show that x y f

quasi polynomials linear diophantine equations and semi linear sets we investigate the family of semi linear sets of n t and z t we study the growth function of semi linear sets and we prove that such a function is a piecewise quasi polynomial on a polyhedral partition of n t moreover we give a new proof of combinatorial character of a famous theorem by dahmen and micchelli on the partition function of a system of diophantine linear equations

elementary contractions of gorenstein threefolds in this paper we show that a generalization of the classification theorem of mori in 113 can be easily obtained from the contraction theorem of 5 a fine analysis is made of the contractions of extremal rays on projective threefolds with normal gorenstein q factorial terminal singularities so that x is in fact factorial a solution of the minimal model problem for threefolds has recently been completed by mori in ll we will first establish notation and give some preliminary results all of the definitions used in this paper can be found in 7 let x be a normal gorenstein projective threefold with q factorial terminal singularities suppose that x is defined over an algebraically closed field k of characteristic zero let r be an extremal ray of x it follows from arguments in 5 or 7 that there is a morphism f x y onto a normal variety y such that f is given by the linear system induced by a cartier divisor h and such that 1 f tp x 9 r 2 for an arbitrary curve c on x d imf c 0 holds if and only if c er 3 the pair f y is uniquely determined by conditions 1 and 2 up to isomorphism 4 s 0 pic y c pic x i sexact for i c i e r

analysis of scattering waves in an elastic layered medium by means of the complete eigenfunction expansion form of the green s function abstract a scattering problem due to an object and a plane incident wave in an elastic layered half space is presented in this paper the complete eigenfunction expansion form of the green s function developed by the author and the boundary integral equation method are introduced into the analysis first the complete eigenfunction expansion form of the green s function is investigated for its application to the scattering problem a comprehensive explanation is also given for the fact that the complex rayleigh wave modes exhibit standing waves next a method for the analysis of scattering waves by means of the green s function is presented the advantage of the present method is that the formulation itself is independent of the number of layers and the scattering waves can be decomposed into the modes for the spectra defined for the layered medium several numerical calculations are performed to examine the efficiency of the present method as well as the properties of the scattering waves according to the numerical results the complete eigenfunction expansion form of the green s function provides accurate values for application to a boundary element analysis the spectral structure and radiation patterns of the scattering wave are presented and investigated the differences in directionality can be found from the radiation patterns of the scattering waves decomposed into the modes for the spectra

a fast volume integral equation method for elastic wave propagation in a half space abstract a fast method for solving the volume integral equation is developed for scattering analysis of elastic wave propagation in a half space the proposed method applies the fast generalized fourier transform and inverse transform formulated in the present study to the krylov subspace method the amount of calculations required for the proposed method is o nlogn where n is the number of grid points used to model the elastic half space furthermore the mpi parallel algorithm for the generalized fourier transform is presented for further reduction of the cpu time numerical calculations are performed in order to examine the effects of the number of sampling grid points as well as their intervals on the solutions of the volume integral equation and the cpu time required for the analysis in addition comparisons of the proposed method with the previous method based on the trapezoidal approach touhei 2009 are also performed in order to discuss the properties of the solution of the present method

on uniruled degenerations of algebraic varieties with trivial canonical divisor we give a uniruledness criterion on degenerate fibers in a family of varieties whose general fiber has a numerically trivial canonical divisor the criterion is related with the so called non nef locus of the canonical divisor of the total space

automorphism groups of positive entropy on minimal projective varieties abstract we determine the geometric structure of a minimal projective threefold having two independent and commutative automorphisms of positive topological entropy and generalize this result to higher dimensional smooth minimal pairs x g as a consequence we give an effective lower bound for the first dynamical degree of these automorphisms of x fitting the boundary case

a fast volume integral equation method for the direct inverse problem in elastic wave scattering phenomena a fast method for solving the volume integral equation is introduced for the solution of forward and inverse multiple scattering problems in an elastic 3 d full space for both forward and inverse scattering analysis the volume integral equation in the wavenumber domain is used by means of the discrete fourier transform the volume integral equation in the wavenumber domain can be dealt with as a fredholm equation of the 2nd kind with respect to a non hermitian operator on a finite dimensional vector space the bi cgstab method is employed to construct the krylov subspace in the wavenumber domain the current procedure establishes a fast and simplified method without requiring the derivation of a coefficient matrix several numerical results validate the accuracy and effectiveness of the current method for both forward and inverse scattering analysis according to the numerical results the reconstruction of inhomogeneities of the wave field is successful even for multiple scattering of several cubes

analytic models and ambiguity of context free languages we establish that several classical context free languages are inherently ambiguous by proving that their counting generating functions when considered as analytic functions exhibit some characteristic form of transcendental behaviour to that purpose we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages in particular the paper contains a general density theorem for unambiguous context free languages

nef dimension of minimal models we reduce the abundance conjecture in dimension 4 to the following numerical statement if the canonical divisor k is nef and has maximal nef dimension then k is big from this point of view we classify in dimension 2 nef divisors which have maximal nef dimension but which are not big

projective uniformization extremal chern classes and quaternionic shimura curves projective structures on compact real manifolds are classical objects in real differential geometry complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than one in the kahler einstein case mathbb p m tori and ball quotients are essentially the only examples they can be described purely in terms of chern class conditions we give a complete classification of all projective manifolds carrying a projective structure the only additional examples are modular abelian families over quaternionic shimura curves they can also be described purely in terms of chern class conditions

on the generating sequences of regular languages on k symbols the main result is a characterization of the generating sequences of the length of words in a regular language on k symbols we say that a sequence s of integers is regular if there is a finite graph g with two vertices i t such that sn is the number of paths of length n from i to t in g thus the generating sequence of a regular language is regular we prove that a sequence s is the generating sequence of a regular language on k symbols if and only if both sequences s sn n 0 and t kn sn n 0 are regular

on birational geometry of minimal threefolds with numerically trivial canonical divisors for a minimal threefold x with k x equiv 0 and a nef and big weil divisor l on x we investigate the birational geometry inspired by l we prove that ml and k x ml give birational maps for all m ge 17 the result remains true under weaker assumption that l is big and has no stable base components

subadditivity of kodaira dimensions for fibrations of three folds in positive characteristics abstract in this paper we will prove subadditivity of kodaira dimensions for a fibration with possibly singular geometric generic fiber under certain nefness and relative semi ampleness conditions as an application for a fibration f x y of a smooth projective threefold over an algebraically closed field of characteristic p 5 under the assumption that y is of general type and non uniruled we prove subadditivity of kodaira dimensions when general fibers are smooth or when k x y is relatively big over y

on the commutative equivalence of semi linear sets of n k given two subsets s 1 s 2 of n k we say that s 1 is commutatively equivalent to s 2 if there exists a bijection f s 1 s s 2 from s 1 onto s 2 such that for every v s 1 v f v where v denotes the sum of the components of v we prove that every semi linear set of n k is commutatively equivalent to a recognizable subset of n k

on algebraic fiber spaces over varieties of maximal albanese dimension we study algebraic fiber spaces f x y where y is of maximal albanese dimension in particular we give an effective version a theorem of kawa mata if pm x 1 for some m 2 then the albanese map of x is surjective combining this with ch it follows that x is birational to an abelian variety if and only if p2 x 1 and q x dim x

on the commutative equivalence of bounded context free and regular languages the semi linear case this is the third paper of a group of three where we prove the following result let a be an alphabet of t letters and let a nt be the corresponding parikh morphism given two languages l1 l2 a we say that l1 is commutatively equivalent to l2 if there exists a bijection f l1 l2 from l1 onto l2 such that for every u l1 u f u then every bounded context free language is commutatively equivalent to a regular language

on the structure of the counting function of sparse context free languages we give an exact description of the counting function of a sparse context free language let l be a sparse context free language and let fl be its counting function then there exist polynomials p0 p1 pk 1 with rational coefficients and an integer constant k0 such that for any n k0 one has fl n pj n where j is such that j n mod k as a consequence one can easily show the decidability of some questions concerning sparse context free languages finally we show that for any sparse context free language l there exists a regular language l such that for any n 0 one has fl n fl n and therefore fl is rational

on irregular threefolds and fourfolds with numerically trivial canonical bundle we prove that for a smooth projective irregular threefold x with k x equiv 0 and a nef and big divisor l on x ml p gives a birational map for all m ge 3 and all p in mathrm pic 0 x we also use the same method to deal with fourfolds and prove that for a smooth projective irregular fourfold x with k x equiv 0 and an ample divisor l on x ml p gives a birational map for all m ge 5 and all p in mathrm pic 0 x these results are optimal

the parikh counting functions of sparse context free languages are quasi polynomials let l be a sparse context free language over an alphabet of t letters and let f l n t n be its parikh counting function we prove the following two results 1 there exists a partition of n t into a finite family of polyhedra such that the function f l is a quasi polynomial on each polyhedron of the partition 2 there exists a partition of n t into a finite family of rational subsets such that the function f l is a polynomial on each set of the partition

viehweg s hyperbolicity conjecture for families with maximal variation we use the theory of hodge modules to construct viehweg zuo sheaves on base spaces of families with maximal variation and fibers of general type and more generally families whose geometric generic fiber has a good minimal model combining this with a result of campana p un we deduce viehweg s hyperbolicity conjecture in this context namely the fact that the base spaces of such families are of log general type this is approached as part of a general problem of identifying what spaces can support hodge theoretic objects with certain positivity properties

on ueno s conjecture k we show that if x is a smooth complex projective variety with kodaira dimension 0 then the kodaira dimension of a general fiber of its albanese map is at most h 0 omega 1 x

strictly nef divisors 0 introduction 565 1 basic definitions known results and main problems 567 2 results in case of non negative kodaira dimension 569 3 the albanese map 572 4 fano fibrations 575 5 birational maps 578 6 higher dimensions 583

a linear sampling method for detecting fluctuations of the wavefield in an elastic half space abstract a linear sampling method for an elastic half space is developed to reconstruct fluctuations in the wavefield the starting point of the formulation is the near field equation that was also used by baganas et al 2006 instead of examining the norm of the solution of the near field equation we define a solvability index in order to obtain the spatial distribution of the amplitude of the solvability index and thus describe the location of the fluctuations a numerical method for the evaluation of the index is also provided for a simplified algorithm this method is based on a projection theorem for a hilbert space and a singular value decomposition numerical calculations were performed and the results validated the efficiency of the proposed method for reconstructing the fluctuations of a wavefield

on the commutative equivalence of bounded context free and regular languages this is the first paper of a group of three where we prove the following result let a be an alphabet of t letters and let a s n t be the corresponding parikh morphism given two languages l 1 l 2 a we say that l 1 is commutatively equivalent to l 2 if there exists a bijection f l 1 s l 2 from l 1 onto l 2 such that for every u l 1 u f u then every bounded context free language is commutatively equivalent to a regular language

bergman kernels and the pseudoeffectivity of relative canonical bundles a criterion for the pseudoeffectivity of twisted relative canonical bundles of surjective projective maps

generalized fourier transform and its application to the volume integral equation for elastic wave propagation in a half space in the present study a generalized fourier transform for time harmonic elastic wave propagation in a half space is developed the generalized fourier transform is obtained from the spectral representation of the operator derived from the elastic wave equation by means of the generalized fourier transform a volume integral equation method for the analysis of scattered elastic waves is presented the proposed method is based on the krylov subspace iteration technique during the iterative process the discrete generalized fourier transform is used where the derivation of a huge and dense matrix from the volume integral equation is not necessary

projectivity of the moduli space of stable log varieties and subadditivity of log kodaira dimension reference epfl article 231100doi 10 1090 jams 871 url http dx doi org 10 1090 jams 871 record created on 2017 09 19 modified on 2017 10 02

pluricanonical maps of varieties of maximal albanese dimension let x be a smooth complex projective algebraic variety of maximal albanese dimension we give a characterization of kappa x in terms of the set v 0 x omega x p in mbox rm pic 0 x h 0 x omega x otimes p ne 0 an immediate consequence of this is that the kodaira dimension kappa x is invariant under smooth deformations we then study the pluricanonical maps varphi m x dashrightarrow mathbb p h 0 x mk x we prove that if x is of general type varphi m is generically finite for m geq 5 and birational for m geq 5 mbox rm dim x 1 more generally we show that for m geq 6 the image of varphi m is of dimension equal to kappa x and for m geq 6 kappa x 2 varphi m is the stable canonical map

uniformisation in dimension four towards a conjecture of iitaka let x be a compact kahler manifold whose universal cover is mathbb c n a conjecture of iitaka claims that some finite etale cover of x is a torus we prove this conjecture in various cases in dimension four we also show that in the projective case iitaka s conjecture is a consequence of the non vanishing conjecture

on the bicanonical map of primitive varieties with q x mathrm dim x the degree and the euler number let x be a variety of maximal albanese dimension and of general type assume that q x mathrm dim x the albanese variety mathrm alb x is a simple abelian variety and the bicanonical map is not birational we prove that the euler number chi x omega x is equal to 1 and 2k x separates two distinct points over the same general point on mathrm alb x via mathrm alb x theorem 1 1

on the abundance theorem in the case of numerical kodaira dimension zero we present a shorter proof of the abundance theorem in the case of numerical kodaira dimension 0 proved by nakayama and its log generalization

building blocks of etale endomorphisms of complex projective manifolds etale endomorphisms of complex projective manifolds are constructed from two building blocks up to isomorphism if the good minimal model conjecture is true they are the endomorphisms of abelian varieties and the nearly etale rational endomorphisms of weak calabi yau varieties

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

on the brody hyperbolicity of moduli spaces for canonically polarized manifolds we show that the moduli stack mh of canonically polarized complex manifolds with hilbert polynomial h is brody hyperbolic hence if mh denotes the corresponding coarse moduli scheme and if u mh is a quasi finite morphism induced by a family then there are no nonconstant holomorphic maps c u

varieties fibered by good minimal models let f x y be an algebraic fiber space such that the general fiber has a good minimal model we show that if f is the iitaka fibration or if f is the albanese map with relative dimension no more than three then x has a good minimal model

two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography abstract this work presents two new volume integral equations for the electroencephalography eeg forward problem which differently from the standard integral approaches in the domain can handle heterogeneities and anisotropies of the head brain conductivity profiles the new formulations translate to the quasi static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems this has been obtained by extending to the volume case the two classical surface integral formulations used in eeg imaging and by introducing an extra surface equation in addition to the volume ones to properly handle boundary conditions numerical results corroborate theoretical treatments showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods