On the singularities and on the projective normality of some Enriques-Fano threefolds

TL;DR

This paper computationally investigates the singularities and projective normality of certain Enriques-Fano threefolds across various genera to aid their classification.

Contribution

It provides new computational insights into the singularities and confirms projective normality for specific Enriques-Fano threefolds, advancing their classification.

Findings

Identified singularities of Enriques-Fano threefolds in genera 6, 7, 8, 9, 10, 13, 17

Established projective normality for these threefolds

Enhanced understanding of their geometric properties

Abstract

In order to find useful information to complete the classification of Enriques-Fano threefolds, we will computationally study the singularities of some known Enriques-Fano threefolds of genus 6, 7, 8, 9, 10, 13 and 17. We will also deduce the projective normality of these threefolds.