Variation of log canonical thresholds in linear systems

TL;DR

This paper studies how log canonical thresholds change within linear systems, providing bounds and insights especially for toric log Fano varieties, linking thresholds to minimal discrepancies.

Contribution

It offers a sharp lower bound for log canonical thresholds of anticanonical members on toric log Fano varieties based on global minimal log discrepancy.

Findings

Established a lower bound for thresholds in toric log Fano varieties

Linked log canonical thresholds to minimal log discrepancy

Enhanced understanding of threshold variation in linear systems

Abstract

We investigate the variation of log canonical thresholds in (graded) linear systems. For toric log Fano varieties, we give a sharp lower bound for log canonical thresholds of the anticanonical members in terms of the global minimal log discrepancy.