Fibered stable varieties

Patakfalvi, Zsolt

doi:10.1090/tran/6386

Fibered stable varieties
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Trans. Amer. Math. Soc. 368 (2016), 1837-1869 Request permission

Abstract:

We show that if a stable variety (in the sense of Kollár and Shepherd-Barron) admits a fibration with stable fibers and base, then this fibration structure deforms (uniquely) for all small deformations. During our proof we obtain a Bogomolov-Sommese type vanishing for vector bundles and reflexive differential $n-1$-forms as well.

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