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Nakano Positivity of direct image sheaves of adjoint line bundles with mild singularities

Yongpan Zou

Abstract

In this note, we generalized Berndtsson's result about the Nakano positivity of direct image sheaves to some special singular cases.

Nakano Positivity of direct image sheaves of adjoint line bundles with mild singularities

Abstract

In this note, we generalized Berndtsson's result about the Nakano positivity of direct image sheaves to some special singular cases.

Paper Structure

This paper contains 8 sections, 18 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Set-up of case $Z$
  3. Nakano positivity via the optimal $L^2$-estimate
  4. Nakano positivity via curvature computation
  5. Set-up of case $V$
  6. the Chern connection
  7. Nakano positivity
  8. Some $L^2$ Hodge theory

Key Result

Theorem 1.1

Under the set-up of case $Z$, the Hermitian holomorphic vector bundle $(\mathcal{F}, \|\cdot\|)$ over $D$ defined in F is semi-positive in the sense of Nakano.

Theorems & Definitions (30)

  • Theorem 1.1
  • Remark 1.2
  • Example 1.3
  • Definition 2.1
  • Theorem 2.2
  • Remark 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Theorem 2.7
  • ...and 20 more