Non-rationality of the symmetric sextic Fano threefold

TL;DR

This paper provides a straightforward proof demonstrating that the symmetric sextic Fano threefold is non-rational, contributing to the understanding of its geometric properties.

Contribution

It offers a simple proof of non-rationality for a specific symmetric sextic Fano threefold, advancing the classification of Fano varieties.

Findings

Proves the non-rationality of the symmetric sextic Fano threefold

Simplifies previous proofs of non-rationality for this class of threefolds

Enhances understanding of the geometric structure of Fano threefolds

Abstract

We give a simple proof of the non-rationality of the Fano threefold defined by the equations \Sigma x_i = \Sigma x_i^2 = \Sigma x_i^3 = 0 in P^6 .