Algebra & Number Theory

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

Sho Ejiri

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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.

Article information

Algebra Number Theory, Volume 13, Number 9 (2019), 2057-2080.

Received: 22 May 2018
Revised: 9 May 2019
Accepted: 13 June 2019
First available in Project Euclid: 14 December 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D06: Fibrations, degenerations
Secondary: 14J45: Fano varieties

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


Ejiri, Sho. Positivity of anticanonical divisors and $F$-purity of fibers. Algebra Number Theory 13 (2019), no. 9, 2057--2080. doi:10.2140/ant.2019.13.2057.

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