Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 9 (2019), 1723-1736.
Birational characterization of Abelian varieties and ordinary Abelian varieties in characteristic
Let be an algebraically closed field of characteristic . We give a birational characterization of ordinary abelian varieties over : a smooth projective variety is birational to an ordinary abelian variety if and only if and . We also give a similar characterization of abelian varieties as well: a smooth projective variety is birational to an abelian variety if and only if , and the Albanese morphism is generically finite. Along the way, we also show that if (or if and is generically finite), then the Albanese morphism is surjective and in particular .
Duke Math. J., Volume 168, Number 9 (2019), 1723-1736.
Received: 28 August 2017
Revised: 9 January 2019
First available in Project Euclid: 12 June 2019
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Hacon, Christopher D.; Patakfalvi, Zsolt; Zhang, Lei. Birational characterization of Abelian varieties and ordinary Abelian varieties in characteristic $p\gt 0$. Duke Math. J. 168 (2019), no. 9, 1723--1736. doi:10.1215/00127094-2019-0008. https://projecteuclid.org/euclid.dmj/1560326500