Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0
| Autor: | Hacon, Christopher D., Patakfalvi, Zsolt, Zhang, Lei |
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| Rok vydání: | 2017 |
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| Zdroj: | Duke Math. J. 168, no. 9 (2019), 1723-1736 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1215/00127094-2019-0008 |
| Popis: | 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 $\kappa_S(X)=0$ and $b_1(X)=2 \dim X$. 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 $\kappa(X)=0$, and the Albanese morphism $a: X \to A$ is generically finite. Along the way, we also show that if $\kappa _S (X)=0$ (or if $\kappa(X)=0$ and $a$ is generically finite) then the Albanese morphism $a:X\to A$ is surjective and in particular $\dim A\leq \dim X$. Comment: This submissium supercedes the previous submission arXiv:1602.01791, 9 pages |
| Databáze: | arXiv |
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