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On vanishing and torsion-freeness results for adjoint pairs

Fanjun Meng

Abstract

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.

On vanishing and torsion-freeness results for adjoint pairs

Abstract

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.

Paper Structure

This paper contains 4 sections, 11 theorems, 59 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Vanishing and torsion-freeness results
  4. Applications

Key Result

Theorem 1.1

Let $f$ be a surjective morphism from a klt pair $(X, \Delta)$ to a normal projective variety $Y$, $L$ a ${\mathbb Q}$-Cartier ${\mathbb Q}$-divisor on $X$ and $\frak{a}$ a nonzero ideal sheaf such that $L\otimes\frak{a}^c$ is nef and $f$-abundant, where $c>0$ is a rational number. Let $D$ be a Cart

Theorems & Definitions (25)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Definition 2.1
  • Proposition 2.2
  • Definition 2.3
  • Definition 2.4
  • Theorem 3.1
  • proof
  • ...and 15 more