Threefolds of globally $F$-regular type with nef anti-canonical divisor

TL;DR

This paper proves that smooth complex projective threefolds with nef anti-canonical divisors are weak Fano if they are of globally F-regular type, confirming a special case of a broader conjecture.

Contribution

It establishes a new link between globally F-regular type and weak Fano property for threefolds, advancing understanding of their geometric classification.

Findings

Smooth complex projective threefolds with nef anti-canonical divisor are weak Fano under globally F-regular type.

Confirms a special case of Schwede and Smith's conjecture.

Provides new insights into the structure of F-regular varieties.

Abstract

As a special case of a conjecture by Schwede and Smith, we prove that a smooth complex projective threefold with nef anti-canonical divisor is weak Fano if it is of globally $F$-regular type.