Vol. 13, No. 9, 2019

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Positivity of anticanonical divisors and $F$-purity of fibers

Sho Ejiri

Vol. 13 (2019), No. 9, 2057–2080
Abstract

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