On some Fano--Enriques threefolds

TL;DR

This paper classifies certain Fano threefolds with specific singularities and involutions, providing insights into Fano--Enriques threefolds and their geometric properties.

Contribution

It offers a new classification of Fano threefolds with canonical Gorenstein singularities and involutions, expanding understanding of Fano--Enriques threefolds.

Findings

Classification of Fano threefolds with involutions

Description of Fano--Enriques threefolds

Analysis of the morphism properties of |-K_X|

Abstract

We give a classification of Fano threefolds $X$ with canonical Gorenstein singularities such that $X$ possess a regular involution, which acts freely on some smooth surface in $|-K_X|$, and the linear system $|-K_X|$ gives a morphism which is not an embedding. From this classification one gets, in particular, a description of some natural class of Fano--Enriques threefolds.