On base point freeness in positive characteristic

Abstract

We prove that if $(X,A+B)$ is a pair defined over an algebraically closed field of positive characteristic such that $(X,B)$ is strongly $F$-regular, $A$ is ample and $K_X+A+B$ is strictly nef, then $K_X+A+B$ is ample. Similarly, we prove that for a log pair $(X,A+B)$ with $A$ being ample and $B$ effective, $K_X+A+B$ is big if it is nef and of maximal nef dimension. As an application, we establish a rationality theorem for the nef threshold and various results towards the minimal model program in dimension three in positive characteristic.

32 pages

References in corpus (3)

• F-thresholds and Bernstein-Sato polynomials
• On the three dimensional minimal model program in positive characteristic
• The trace map of Frobenius and extending sections for threefolds

Cited by in corpus (4)

• Test ideals in rings with finitely generated anti-canonical algebras
• On base point free theorem of threefolds in positive characteristic
• Iitaka's $C_{n,m}$ conjecture for 3-folds over finite fields
• On Rational Connectedness of Globally F-Regular Threefolds