2015•Transactions of the American Mathematical SocietyOpen access
Fibered stable varieties
Zsolt Patakfalvi
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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 n-1 -forms as well.
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