From H\"ormander's $L^2$-estimates to partial positivity

TL;DR

This paper introduces new characterizations of partial positivity in complex geometry using a twisted H"ormander's $L^2$-estimate, focusing on uniform $q$-positivity and RC-positivity, including for singular metrics.

Contribution

It provides novel characterizations of partial positivity notions via a twisted H"ormander's $L^2$-estimate, expanding understanding of positivity in complex geometry.

Findings

New characterizations of partial positivity

Extension of uniform $q$-positivity to singular metrics

Discussion on the definition of uniform $q$-positivity for singular Hermitian metrics

Abstract

In this article, using a twisted version of H\"ormander's $L^2$-estimate, we give new characterizations of notions of partial positivity, which are uniform $q$-positivity and RC-positivity. We also discuss the definition of uniform $q$-positivity for singular Hermitian metrics.