Positivity of anticanonical divisors and F-purity of fibers

We prove that given a flat generically smooth morphism between smooth projective varieties with $F$ - pure closed fibers, if the source space is Fano, weak Fano or a variety with nef anticanonical divisor, respectively, then so is the target space. We also show that, in arbitrary characteristic, a generically smooth surjective morphism between smooth projective varieties cannot have nef and big relative anticanonical divisor, if the target space has positive dimension.

Keywords

Fano variety, weak Fano variety, anticanonical divisor, restricted base locus, augmented base locus

Mathematical Subject Classification 2010

Primary: 14D06

Secondary: 14J45

Milestones

Received: 22 May 2018

Revised: 9 May 2019

Accepted: 13 June 2019

Published: 7 December 2019

Authors

Sho Ejiri
Department of Mathematics Graduate School of Science Osaka University Japan

Vol. 13, No. 9, 2019

Sho Ejiri

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors