Rationality of Fano threefolds with terminal Gorenstein singularities, I

TL;DR

This paper classifies certain non-rational Fano threefolds with terminal Gorenstein singularities, specifically identifying all hyperelliptic and trigonal varieties within this class.

Contribution

It provides a classification of non-rational Fano threefolds with terminal Gorenstein singularities, focusing on hyperelliptic and trigonal cases, which was previously unexplored.

Findings

All hyperelliptic Fano threefolds with terminal Gorenstein singularities identified.

All trigonal Fano threefolds with terminal Gorenstein singularities identified.

Classification results contribute to understanding the structure of Fano threefolds with singularities.

Abstract

We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.