On the rational Enriques-Fano threefolds discovered by Fano

TL;DR

This paper revisits Fano's classification of Enriques-Fano threefolds, addressing gaps in his original arguments by applying modern mathematical techniques to verify his assertions.

Contribution

The paper provides a rigorous verification of Fano's claims on Enriques-Fano threefolds using contemporary methods, clarifying and solidifying the classification.

Findings

Confirmed Fano's assertions on certain Enriques-Fano threefolds.

Identified and addressed gaps in Fano's original arguments.

Enhanced the understanding of the structure of Enriques-Fano threefolds.

Abstract

It was Fano who first classified Enriques-Fano threefolds. However his arguments appear to contain several gaps. In this paper, we will verify some of his assertions through the use of modern techniques.