Fano varieties with large Seshadri constants in positive characteristic
Annales de l'Institut Fourier, Volume 72 (2022) no. 2, pp. 685-725.

We prove that a Fano variety (with arbitrary singularities) of dimension n in positive characteristic is isomorphic to n if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than n and classify Fano varieties whose anti-canonical divisors have Seshadri constants n. In characteristic p>5 and dimension 3, we also show that Fano varieties X with Seshadri constants ϵ(-K X ,x)>2+ϵ at some smooth point xX (for some fixed ϵ>0) have bounded anti-canonical degrees.

Nous prouvons qu’une variété de Fano (avec des singularités arbitraires) de dimension n en caractéristique positive est isomorphe à n , si la constante de Seshadri du diviseur anti-canonique en un point lisse est supérieure à n. Nous classons les variétés de Fano dont les constantes de Seshadri des diviseurs anti-canoniques sont égales à n. En caractéristique p>5 et en dimension 3, nous montrons également que les degrés anti-canoniques d’une variété de Fano X avec des constantes de Seshadri ϵ(-K X ,x)>2+ϵ en un certain point lisse x (pour un certain ϵ>0 fixé) sont bornés.

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Accepted:
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DOI: 10.5802/aif.3477
Classification: 14J45,  14E99,  14C20,  14G17
Keywords: Fano variety, Seshadri constant, positive characteristic, boundedness, classification
Zhuang, Ziquan 1

1 Department of Mathematics, MIT Cambridge, MA, 02139, USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Zhuang, Ziquan. Fano varieties with large Seshadri constants in positive characteristic. Annales de l'Institut Fourier, Volume 72 (2022) no. 2, pp. 685-725. doi : 10.5802/aif.3477. https://aif.centre-mersenne.org/articles/10.5802/aif.3477/

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