On terminal Fano 3-folds with 2-torus action, part II

TL;DR

This paper advances the classification of terminal Fano threefolds with two-torus actions by focusing on the broader class of combinatorially minimal varieties that lack prime divisor contractions.

Contribution

It extends previous work by classifying non-Q-factorial terminal Fano threefolds with two-torus actions, specifically those that are combinatorially minimal.

Findings

Classification of combinatorially minimal terminal Fano threefolds completed

Identification of properties distinguishing these varieties from Q-factorial cases

Expansion of the known landscape of Fano threefolds with torus actions

Abstract

We continue the classification of terminal Fano threefolds with an effective two-torus action. In earlier work we settled the Q-factorial case with Picard number one. Here we treat the larger class of varieties that do not admit any contraction of a prime divisor; these are called combinatorially minimal.