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15 June 2019 Birational characterization of Abelian varieties and ordinary Abelian varieties in characteristic p>0
Christopher D. Hacon, Zsolt Patakfalvi, Lei Zhang
Duke Math. J. 168(9): 1723-1736 (15 June 2019). DOI: 10.1215/00127094-2019-0008

Abstract

Let k be an algebraically closed field of characteristic p>0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if κS(X)=0 and b1(X)=2dimX. We also give a similar characterization of abelian varieties as well: a smooth projective variety X is birational to an abelian variety if and only if κ(X)=0, and the Albanese morphism a:XA is generically finite. Along the way, we also show that if κS(X)=0 (or if κ(X)=0 and a is generically finite), then the Albanese morphism a:XA is surjective and in particular dimAdimX.

Citation

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Christopher D. Hacon. Zsolt Patakfalvi. Lei Zhang. "Birational characterization of Abelian varieties and ordinary Abelian varieties in characteristic p>0." Duke Math. J. 168 (9) 1723 - 1736, 15 June 2019. https://doi.org/10.1215/00127094-2019-0008

Information

Received: 28 August 2017; Revised: 9 January 2019; Published: 15 June 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07097313
MathSciNet: MR3961214
Digital Object Identifier: 10.1215/00127094-2019-0008

Subjects:
Primary: 14E99
Secondary: 14K05, 14K15

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 9 • 15 June 2019
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