Fano varieties with conjecturally largest Fano index

TL;DR

This paper constructs examples of Fano varieties with large Fano index across various singularities and conjectures these examples have the maximal Fano index in all dimensions based on low-dimensional evidence.

Contribution

It introduces new examples of Fano varieties with large Fano index and proposes a conjecture about their maximality across all dimensions.

Findings

Constructed examples of Fano varieties with large Fano index

Conjecture that these examples have the largest Fano index in all dimensions

Evidence based on low-dimensional cases

Abstract

For Fano varieties of various singularities such as canonical and terminal, we construct examples with large Fano index. By low-dimensional evidence, we conjecture that our examples have the largest Fano index for all dimensions.