Algebra & Number Theory
- Algebra Number Theory
- Volume 13, Number 9 (2019), 2057-2080.
Positivity of anticanonical divisors and $F$-purity of fibers
We prove that given a flat generically smooth morphism between smooth projective varieties with - 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.
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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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. https://projecteuclid.org/euclid.ant/1576292485