Vanishing theorems.
Vanishing theorems for constructible sheaves I.
Vanishing theorems for tensor powers of an ample vector bundles.
Vanishing Theorems for the Intersection Homology of Stein Spaces.
Vanishing theorems, linear and quadratic normality.
Vanishing theorems on cohomology associated to hermitian symmetric spaces
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.
Vanishing Theorems on Compact Hermitian Symmetric Spaces.
Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians
In this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.
Vector bundles on manifolds without divisors and a theorem on deformations
We study holomorphic vector bundles on non-algebraic compact manifolds, especially on tori. We exhibit phenomena which cannot occur in the algebraic case, e.g. the existence of 2-bundles that cannot be obtained as extensions of a sheaf of ideals by a line bundle. We prove some general theorems in deformations theory of bundles, which is our main tool.
Vector bundles on non-Kaehler elliptic principal bundles
We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.
Vector Bundles on Projective 3-Space.
Vector bundles with trivial determinant and second Chern class one on some non-Kähler surfaces.
Vector Fields and Chern Numbers.
Vector fields on the Sato Grassmannian.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.
Vector fields, residues and cohomology
Vektorbündel vom Rang 2 über dem n-dimensionalen komplex-projektiven Raum.
Vektorraumbündel über nichtarchimedischen holomorphen Räumen.
Verschwindungssätze und Untermannigfaltigkeiten kleiner Kodimension des komplex-projektiven Raumes.
Versions kählériennes du théorème d'annulation de Bogomolov.
We extend to compact Kaehler and Fujiki manifolds the theorem of F. Bogomolov, on vanishing of the space of holomorphic p-forms with values in a line bundle whose dual L is numerically effective, for the degrees p less than the numerical dimension of L.