Boundedness of log terminal Fano pairs of bounded index

TL;DR

This paper proves that Fano varieties with Kawamata log terminal singularities and a fixed index form a bounded family, confirming a conjecture by Batryev and advancing understanding of their classification.

Contribution

It establishes the boundedness of Fano varieties with fixed index and Kawamata log terminal singularities, confirming Batryev's conjecture.

Findings

Fano varieties with fixed index are bounded in families.

Confirmed Batryev's conjecture on boundedness.

Advances classification of singular Fano varieties.

Abstract

We prove a conjecture of Batryev which states that the family of all Fano varieties with kawamata log terminal singularities and fixed index, forms a bounded family.