A rationality criterion for real Fano threefolds

TL;DR

This paper investigates the conditions under which smooth geometrically rational Fano threefolds over the real numbers are rational, providing a new criterion based on the connectedness of their real points.

Contribution

It introduces a sufficient criterion for the real rationality of Fano threefolds, linking geometric properties to rationality over the real numbers.

Findings

Connectedness of the real locus implies rationality in certain cases.

Established a new criterion for real rationality of Fano threefolds.

Provided examples illustrating the criterion's application.

Abstract

We study the connectedness of the real locus of smooth geometrically rational Fano threefolds and prove a sufficient criterion of $\mathbb{R}$-rationality.