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

TL;DR

This paper extends Berndtsson's results on the Nakano positivity of direct image sheaves to include certain singular cases, broadening the understanding of positivity properties in complex geometry.

Contribution

It introduces a generalization of Nakano positivity results to direct image sheaves with mild singularities, expanding the applicability of previous positivity theorems.

Findings

Established Nakano positivity for direct image sheaves with mild singularities.

Extended Berndtsson's positivity results to new singular cases.

Provided theoretical framework for positivity in singular settings.

Abstract

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