Related papers: Vanishing theorems for locally conformal hyperkaeh…

Andreotti-Vesentini, Ohsawa, Gromov, Koll\'ar, among others, have observed that Hodge theory could be extended to (non compact) K\"ahler complete manifolds, within the L^2 framework. Also, many vanishing theorems on projective or K\"ahler…

Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that $H^j(X,\Omega^i_X\otimes L)=0$ for every $j>0$, $i\geq 0$, and $L$ ample. This holds for toric varieties, but not for most other varieties. We…

In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kaehler (or shortly l.c.K.) manifold, a holomorphic structure theorem asserting that it has a structure of holomorphic principal fiber…

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 derive sufficient conditions for the vanishing of plurigenera, $p_m(J), m>0$, on compact (l|k)-strong, $\omega^l\wedge \partial\bar\partial \omega^k=0$, Kaehler manifolds with torsion. In particular, we show that the plurigenera of…

Let $X$ be a closed equidimensional local complete intersection subscheme of a smooth projective scheme $Y$ over a field, and let $X_t$ denote the $t$-th thickening of $X$ in $Y$. Fix an ample line bundle $\mathcal{O}_Y(1)$ on $Y$. We prove…

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,…

Suppose $\Cal R$ is the complement of an essential arrangement of toric hyperlanes in the complex torus $(\C^*)^n$ and $\pi=\pi_1(\Cal R)$. We show that $H^*(\Cal R;A)$ vanishes except in the top degree $n$ when $A$ is one of the following…

We study Kahler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge2$ boundary components (possibly $l=\infty$), then it has first betti…

We prove a vanishing theorem of Betti numbers on compact, strictly pseudoconvex pseudohermitian manifolds with non-negative curvature operator. The proof is by an application of the Bochner technique to the setting of CR manifolds.

Let X be a Zariski open subset of a compact Kaehler manifold. In this paper, we study the set $\Sigma^k(X)$ of one dimensional local systems on X with nonvanishing kth cohomology. We show that under certain conditions (X compact, X has a…

A locally conformally Kaehler (LCK) manifold is a complex manifold admitting a Kaehler covering M, with monodromy acting on M by Kaehler homotheties. A compact LCK manifold is Vaisman if it admits a holomorphic flow acting by non-trivial…

The main result is that for a connected hyperbolic complete K\"ahler manifold with bounded geometry of order two and exactly one end, either the first compactly supported cohomology with values in the structure sheaf vanishes or the…

This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…

For compact K\"ahlerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry…

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…

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…

A linear constraint is given on the Betti numbers of a compact hyper-Kaehler manifold, using an index formula for c_1c_{n-1} on an almost complex manifold. The topology of some other manifolds with reduced holonomy is also discussed…

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is…

Let $(R,\fr m)$ be a Noetherian local ring, $I$ an ideal of $R$ and $M, N$ two finitely generated $R$-modules. The first result of this paper is to prove a vanishing theorem for generalized local cohomology modules which says that…