On quasi-log structures for complex analytic spaces

TL;DR

This paper introduces quasi-log structures for complex analytic spaces, establishing their fundamental properties and linking them to semi-log canonical pairs, advancing the minimal model theory in complex geometry.

Contribution

It defines quasi-log complex analytic spaces and proves their properties, connecting them to semi-log canonical pairs, advancing minimal model theory for complex analytic spaces.

Findings

Quasi-log complex analytic spaces are well-defined and have fundamental properties.

Semi-log canonical pairs naturally admit quasi-log structures.

Progress towards a minimal model theory for complex analytic spaces.

Abstract

We introduce the notion of quasi-log complex analytic spaces and establish various fundamental properties. Moreover, we prove that a semi-log canonical pair naturally has a quasi-log complex analytic space structure. This paper is part of the author's project to establish a minimal model theory for projective morphisms between complex analytic spaces.