Related papers: Vanishing theorems for generalized pairs
We prove the Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs. We also give a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.
We give an alternative proof of Kov\'acs' vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kov\'acs' vanishing theorem to the well-known…
We use Koll\'ar's gluing theory to prove the contraction theorem for generalized pairs. In particular, we show that we can run the MMP for any generalized log canonical pairs.
We prove the Kawamata-Viehweg vanishing theorem for a large class of divisors on surfaces in positive characteristic. By using this vanishing theorem, Reider-type theorems and extension theorems of morphisms for normal surfaces are…
This is a short report on our new vanishing theorems for projective morphisms between complex analytic spaces. We established a complex analytic generalization of Koll\'ar's torsion-freeness and vanishing theorem for analytic simple normal…
We prove some injectivity, torsion-free, and vanishing theorems for simple normal crossing pairs. Our results heavily depend on the theory of mixed Hodge structures on compact support cohomology groups. We also treat several basic…
The first part of the paper contains a detailed proof of M. Saito's generalization of the Kodaira vanishing theorem, following the original argument and with ample background, based on a lecture given at a Clay workshop on mixed Hodge…
This is a sequel to "Kodaira-Saito vanishing via Higgs bundles in positive characteristic" (arXiv:1611.09880). However, unlike the previous paper, all the arguments here are in characteristic zero. The main result is a Kodaira vanishing…
A Lie algebroid is a generalization of Lie algebra that provides a general framework to describe the symmetries of a manifold. In this paper, we generalize the Kodaira vanishing theorem, which is a basic result in complex geometry, to…
We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…
We propose a new formulation of a vanishing theorem for surfaces. Although this vanishing theorem follows easily from the well-known Kawamata--Viehweg vanishing theorem, it turns out to be remarkably useful. In particular, it is sufficient…
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 prove that the non-vanishing conjecture holds for generalized lc pairs with a polarization.
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…
We prove some vanishing and torsion-freeness results for higher direct images of adjoint pairs satisfying relative abundance and nefness conditions. These are applied to generic vanishing and weak positivity.
We associate to a pair $(X,D)$, consisting of a smooth scheme with a divisor $D\in \text{Div}(X)\otimes \mathbb{Q}$ whose support is a divisor with normal crossings, a canonical Deligne--Mumford stack over $X$ on which $D$ becomes integral.…
We give an analytic proof of the Saito vanishing theorem using $L^{2}$-methods, by going back to the original idea for the proof of the Kodaira vanishing theorem.
This paper contains a Kawamata-Viehweg-Koll\'ar type vanishing theorem for vector bundles. In order to formulate and prove this cleanly, we introduce a class of sheaves that automatically satisfies a vanishing theorem. This is obtained by…
In the present paper, we establish a general Kawamata-Viehweg-Koll\'ar-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact K\"ahler manifolds, unifying a number of…
We prove a relative Kawamata Viehweg vanishing type theorem for birational morphisms. We use this to prove a Grauert Riemenschneider theorem over log canonical threefolds without zero dimensional log canonical centers, in residue…