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July 2020 Smoothing of semistable Fano varieties
Junchao Shentu
Osaka J. Math. 57(3): 617-645 (July 2020).

Abstract

In this paper we study the smoothing of a semistable Fano variety over a perfect field $k$. In characteristic 0, the reduced semistable Fano degenerate fibers of Mori fibrations are classified. In positive characteristic, under a suitable $W_2$ lifting assumption, we prove that a semistable Fano variety always appears as a degenerate fiber in a semistable family if it has a global log structure (in the sense of Fontaine-Illusie-Kato) of semistable type. A geometric criterion for the existence of a log structure of semistable type is given.

Citation

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Junchao Shentu. "Smoothing of semistable Fano varieties." Osaka J. Math. 57 (3) 617 - 645, July 2020.

Information

Published: July 2020
First available in Project Euclid: 13 July 2020

zbMATH: 07224924
MathSciNet: MR4121779

Subjects:
Primary: 13D10, 14F17

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics

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Vol.57 • No. 3 • July 2020
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