On Gorenstein Fano Threefolds with an Action of a Two-Dimensional Torus

TL;DR

This paper classifies certain special Fano threefolds that are non-toric, Gorenstein, and admit a two-dimensional torus action, expanding understanding of their structure and symmetries.

Contribution

It provides a classification of non-toric, Gorenstein Fano threefolds with a two-dimensional torus action, focusing on those with Picard number one.

Findings

Classification of non-toric Gorenstein Fano threefolds with torus action

Identification of conditions for $Q$-factoriality and log terminal singularities

Explicit description of the torus actions on these threefolds

Abstract

We classify the non-toric, $\mathbb Q$-factorial, Gorenstein, log terminal Fano threefolds of Picard number one that admit an effective action of a two-dimensional algebraic torus.