An effective upper bound for Fano indices of canonical Fano threefolds, I

TL;DR

This paper establishes a new upper bound of 61 for the $Q$-Fano index of $Q$-factorial weak Fano threefolds with isolated canonical singularities, advancing understanding of their classification.

Contribution

The paper introduces a sharp upper bound for the Fano index of certain threefolds, providing a key constraint in their classification theory.

Findings

Fano index of such threefolds is at most 61

Provides a bound that aids in classification efforts

Advances understanding of canonical Fano threefolds

Abstract

Let $X$ be a $\mathbb Q$-factorial weak Fano $3$-fold with at worst isolated canonical singularities. We show that the $\mathbb Q$-Fano index of $X$ is at most $61$.