Related papers: On direct images of pluricanonical bundles
We present an effective global generation result for direct images of pluricanonical bundles in mixed characteristic. This is a mixed characteristic analog of Ejiri's theorem in positive characteristic and the theorem of Popa and Schnell…
In this paper, we study pushforwards of log pluricanonical bundles on projective log canonical pairs $(Y,\Delta)$ over the complex numbers, partially answering a Fujita-type conjecture due to Popa and Schnell in the log canonical setting.…
We study the Fujita-type conjecture proposed by Popa and Schnell. We obtain an effective bound on the global generation of direct images of pluri-adjoint line bundles on the regular locus. We also obtain an effective bound on the generic…
We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…
We study the relationship between positivity of line bundles restricted to complete intersection subvarieties and the vanishing of higher cohomology groups. Based on this connection we prove generalizations of the vanishing theorems of…
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…
In this paper, we study an algebraic fiber space in positive characteristic whose generic fiber $F$ has finitely generated canonical ring and sufficiently large Frobenius stable canonical ring. An example of such a case is when $F$ is…
Our main goal in this article is to establish a quantitative version of the positivity properties of twisted relative pluricanonical bundles and their direct images. The notion of "singular Hermitian metric" on vector bundles (together with…
In the first part of the paper, we study a Fujita-type conjecture by Popa and Schnell, and give an effective bound on the generic global generation of the direct image of the twisted pluricanonical bundle. We also point out the relation…
We describe examples showing the sharpness of Fujita's conjecture on adjoint bundles also in the general type case, and use these examples to formulate related bold conjectures on pluricanonical maps of varieties of general type.
In this note, we generalize slightly Popa--Schnell's theorem regarding to direct images of pluricanonical bundles to the case when the ample line bundle is not globally generated. We also treat the case of positive characteristic.
Generalizing the recent result of Berndtsson, we prove the Nakano semipositivity of the direct image of relative pluricanonical systems and the direct image of relative adjoint (singular) hermitian line bundle with semipositive curvature.…
In the first part of this paper we prove a vanishing criterion for higher direct images of projective families of line bundles on a Cohen-Macaulay variety X. The result involves certain first-order deformations of certain curves on X, and…
In this paper, we investigate higher direct images of log canonical divisors. After we reformulate Koll\'ar's torsion-free theorem, we treat the relationship between higher direct images of log canonical divisors and the canonical…
The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension…
In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which…
Given a proper holomorphic surjective morphism $f:X\rightarrow Y$ from a compact K\"ahler manifold to a compact K\"ahler manifold, and a Nakano semipositive holomorphic vector bundle $E$ on $X$, we prove Koll\'ar type vanishing theorems on…
We study cohomology support loci and higher direct images of (log) pluricanonical bundles of smooth projective varieties or log canonical pairs. We prove that the 0-th cohomology support loci of log pluricanonical bundles are finite unions…
For proper surjective holomorphic maps from K"ahler manifolds to analytic spaces, we give a decomposition theorem for the cohomology groups of the canonical bundle twisted by Nakano semi-positive vector bundles by means of the higher direct…
We give an overview of partial positivity conditions for line bundles, mostly from a cohomological point of view. Although the current work is to a large extent of expository nature, we present some minor improvements over the existing…