On Rational Connectedness of Globally F-Regular Threefolds

TL;DR

This paper proves that projective globally F-regular threefolds over algebraically closed fields of characteristic at least 11 are rationally chain connected, advancing understanding of their geometric properties.

Contribution

It establishes the rational chain connectedness of globally F-regular threefolds in characteristic p ≥ 11, a significant step in positive characteristic algebraic geometry.

Findings

Globally F-regular threefolds are rationally chain connected.

The result holds over algebraically closed fields of characteristic p ≥ 11.

Advances the classification of F-regular varieties in positive characteristic.

Abstract

In this paper, we show that projective globally $F$-regular threefolds, defined over an algebraically closed field of characteristic $p\geq 11$, are rationally chain connected.