Fano varieties with large Seshadri constants

TL;DR

This paper investigates Fano varieties with large Seshadri constants, establishing boundedness properties and classifying certain singular Fano varieties based on their Seshadri constants.

Contribution

It extends previous classifications by analyzing Fano varieties with large Seshadri constants, including those with arbitrary singularities, and proves boundedness results.

Findings

Fano varieties with large Seshadri constants are weakly and birationally bounded.

Classified singular Fano varieties of dimension n with Seshadri constants at least n.

Generalizes earlier results by Liu and the author.

Abstract

We show that the set of Fano varieties (with arbitrary singularities) whose anticanonical divisors have large Seshadri constants satisfies certain weak and birational boundedness. We also classify singular Fano varieties of dimension $n$ whose anticanonical divisors have Seshadri constants at least $n$, generalizing an earlier result of Liu and the author.