Related papers: Sommese Vanishing for non-compact manifolds

We prove a Serre type vanishing property for the twisted primitive cohomology of a symplectic manifold. It is based on Tseng and Zhou's vanishing property under the symplectic flatness. These vanishing properties emphasizes the necessity of…

In this note we show a Kawamata-Viehweg vanishing theorem for pl-contractions on threefolds in characteristic $p>5$. We deduce several applications for klt threefolds: the vanishing of higher direct images of structure sheaves of Mori fibre…

We establish the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As a consequence, we provide a new proof of the base-point-freeness theorem for lc generalized pairs. This new approach allows…

We prove a general criterion for the vanishing of second bounded cohomology (with trivial real coefficients) for groups that admit an action satisfying certain mild hypotheses. This leads to new computations of the second bounded cohomology…

In chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such…

We obtain the Bogomolov-Sommese type vanishing theorem involving multiplier ideal sheaves for big line bundles. We define a dual Nakano semi-positivity of singular Hermitian metrics with L2-estimates and prove the vanishing theorem which is…

We generalize the torsion vanishing results of Caraiani-Scholze and Koshikawa. Our results apply to the cohomology of general Shimura varieties $(\mathbf{G},X)$ of PEL type $A$ or $C$, localized at a suitable maximal ideal $\mathfrak{m}$ in…

Given an embedded smooth projective variety Y in CP^n, we show how the existence of a hypersurface with high multiplicity along Y, but of relatively low degree and log canonical near Y implies vanishing of higher cohomology for certain…

We use homological methods to establish a formal criterion for Generic Vanishing, in the sense originated by Green and Lazarsfeld and pursued further by Hacon and the first author, but in the context of an arbitrary Fourier-Mukai…

Considering modules of finite complete intersection dimension over commutative Noetherian local rings, we prove (co)homology vanishing results in which we assume the vanishing of nonconsecutive (co)homology groups. In fact, the (co)homology…

We use Cox's description for sheaves on toric varieties and results about the local cohomology with respect to monomial ideals to give a characteristic free approach to vanishing results on arbitrary toric varieties. As an application, we…

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

This work discusses combinatorial and arithmetic aspects of cohomology vanishing for divisorial sheaves on toric varieties. We obtain a refined variant of the Kawamata-Viehweg theorem which is slightly stronger. Moreover, we prove a new…

We establish cosection localization and vanishing results for virtual fundamental classes of derived manifolds, combining the theory of derived differential geometry by Joyce with the theory of cosection localization by Kiem-Li. As an…

Chain total double complexes with reductive differentials for non-abelian simplexes with associated spaces are considered. It is conjectured that corresponding relative cohomology is equivalent to the coset space of vanishing over…

In this paper we will first show some Kollar-Enoki type injectivity theorems on compact Kahler manifolds, by using the Hodge theory, the Bochner- Kodaira-Nakano identity and the analytic method provided by O. Fujino and S. Matsumura in [15,…

It is known that the semisimplicity of quantum cohomology implies the vanishing of off-diagonal Hodge numbers (Hodge--Tateness). We investigate which hyperplane sections of homogeneous varieties possess either of the two properties. We…

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly…

We study a singular Hermitian metric of a vector bundle. First, we prove the sheaf of locally square integrable holomorphic sections of a vector bundle with a singular Hermitian metric, which is a higher rank analogy of a multiplier ideal…

In this paper we find sufficient conditions for the vanishing of the Morse-Novikov cohomology on Riemannian foliations. We work out a Bochner technique for twisted cohomological complexes, obtaining corresponding vanishing results. Also, we…