Infinitesimal variations of hodge structure (I)
Invariance for multiples of the twisted canonical bundle
Let a smooth projective family and a pseudo-effective line bundle on (i.e. with a non-negative curvature current ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of (defined over the central fiber of the family ) to sections of . In this article we consider the following problem: to extend sections of . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf , any section of extends to ; in other...
extension of adjoint line bundle sections
We prove an extension theorem of Ohsawa-Takegoshi type for line bundle sections on a subvariety of general codimension in a normal projective variety. Our method of proof gives conditions to be satisfied for such extension in a general setting, while such conditions are satisfied when the subvariety is given by an appropriate multiplier ideal sheaf.
Local cohomology of sheaves of differential forms and Hodge theory.
Méthodes et résultats effectifs en géométrie algébrique
Métriques de Quillen et plongements complexes
Milnor numbers and the topology of polynomial hypersurfaces.
Minimal varieties with trivial canonical classes, I.
Mixed Hodge theory for unitary local systems.
Nondeformability of the complex hyperquadric.
Normal affine surfaces properly dominated by C x C.
Numerically trivial foliations
Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kähler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji’s numerically trivial fibration and the Iitaka fibration. Using almost positive singular hermitian metrics with analytic singularities on a pseudo-effective line bundle , a foliation is constructed refining the nef fibration. If the singularities of the foliation are...
Offenheit der Versalität in der analytischen Geoemtrie.
On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.
On Bloch's Conjecture.
On Compact Analytic Threefolds with Non-Trivial Albanese Tori.
On Compactifiable Complex Analytic Surfaces.
On Complexifications of Differentiable Manifolds.
On Deformations of Kähler Spaces. I.
On Deformations of Threedimensional Rational Manifolds.