Wall crossing for moduli of stable log pairs

TL;DR

This paper establishes the existence of wall-crossing and reduction morphisms for moduli spaces of stable log pairs across all dimensions, as the divisor coefficients vary, advancing the understanding of their geometric structure.

Contribution

It proves the existence of wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions, under suitable conditions.

Findings

Wall-crossing morphisms are shown to exist in all dimensions.

Reduction morphisms are established for moduli spaces of stable log pairs.

The results depend on certain suitable conditions for the coefficients.

Abstract

We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients of the divisor.