Related papers: On a vanishing theorem due to Bogomolov

Given scheme-theoretic equations for a nonsingular subvariety, we prove that the higher cohomology groups for suitable twists of the corresponding ideal sheaf vanish. From this result, we obtain linear bounds on the multigraded…

We give a proof of a conjecture raised by Michael Finkelberg and Andrei Ionov. As a corollary, the coefficients of multivariable version of Kostka functions introduced by Finkelberg and Ionov are non-negative.

We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.

In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.

We establish strong vanishing theorems for line bundles on wonderful varieties of hyperplane arrangements, and we show that the resulting positivity properties of Euler characteristics extend to all matroids. We achieve this by showing that…

Let M^7 a manifold with holonomy in G_2, and Y^3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that M_{X,Y}, the moduli space of its associative deformations with boundary in the fixed…

We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…

Griffiths and Harris showed in 1978 that if E is a rank n vector bundle on a smooth projective variety of dimension n, and if s is a section of E vanishing simply on a finite set Z, then any section of (K_X + det E) vanishing at all but one…

In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This…

This paper reproves a general form of the Green-Lazarsfeld 'generic vanishing' theorem and more recent strengthenings, as well as giving some new applications.

We show that compact K\"ahler manifolds have the rational cohomology ring of complex projective space provided a weighted sum of the lowest three eigenvalues of the K\"ahler curvature operator is positive. This follows from a more general…

Using the framework of noncommutative Kahler structures, we generalise to the noncommutative setting the celebrated vanishing theorem of Kodaira for positive line bundles. The result is established under the assumption that the associated…

Inspired by the methods of Voisin, the first two authors recently proved that one could read off the gonality of a curve C from the syzygies of its ideal in any one embedding of sufficiently large degree. This was deduced from from a…

The purpose of this paper is to establish a Nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's…

We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex…

We study numerical restricted volumes of (1,1) classes on compact Kahler manifolds, as introduced by Boucksom. Inspired by work of Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricted volumes of line bundles on projective manifolds, we pose a…

In view of A. Andreotti and H. Grauert's vanishing theorem for q-complete domains in C^n, (Th\'eor\`eme de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193--259,) we re-prove a vanishing result by…

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

This work establishes a structure theorem for compact K\"ahler manifolds with semipositive anticanonical bundle. Up to finite \'etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat…

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…