On the Rationality of Fano-Enriques Threefolds

TL;DR

This paper investigates the birational geometry and rationality of Fano-Enriques threefolds, a class of non-Gorenstein Fano varieties with specific singularities, and provides an example with high pliability.

Contribution

It offers new insights into the rationality of Fano-Enriques threefolds and constructs an example with pliability equal to 9, highlighting their complex birational structure.

Findings

Analyzed the birational properties of Fano-Enriques threefolds.

Provided an explicit example with pliability 9.

Enhanced understanding of the rationality of these varieties.

Abstract

A Fano-Enriques threefold is a three-dimensional non-Gorenstein Fano variety of index 1 with at most canonical singularities. We study the birational geometry of Fano-Enriques threefolds with terminal cyclic quotient singularities. We investigate their rationality, and also provide an example of a Fano-Enriques threefold, whose pliability is 9, i.e. a Fano-Enriques threefold birationally equivalent to exactly 9 Mori fibre spaces in Sarkisov category.