Minimal log discrepancies of regularity one

TL;DR

This paper investigates minimal log discrepancies of regularity one using nef cones, improving nef cone theorems, establishing ascending chain conditions, and providing bounds for singularities.

Contribution

It introduces new bounds and conditions for minimal log discrepancies of regularity one, advancing understanding of their behavior in algebraic geometry.

Findings

Improved nef cone theorem for log Calabi-Yau dlt pairs

Established ascending chain condition around zero for these discrepancies

Proved existence of an upper bound for minimal log discrepancies of regularity one

Abstract

In this article, we use the cone of nef curves to study minimal log discrepancies. The first result is an improvement of the nef cone theorem in the case of log Calabi-Yau dlt pairs. Then, we prove that the ascending chain condition for $n$-dimensional minimal log discrepancies of regularity one holds around zero. Furthermore, we show that there exists an upper bound for the minimal log discrepancy of any $n$-dimensional klt singularity of regularity one.