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Transactions of the American Mathematical Society

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Fibered stable varieties

Author: Zsolt Patakfalvi
Journal: Trans. Amer. Math. Soc. 368 (2016), 1837-1869
MSC (2010): Primary 14J10; Secondary 14J40
Published electronically: June 15, 2015
MathSciNet review: 3449226
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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$-forms as well.

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Additional Information

Zsolt Patakfalvi
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000

Received by editor(s): April 13, 2013
Received by editor(s) in revised form: June 20, 2013, September 17, 2013, January 6, 2014, and January 8, 2014
Published electronically: June 15, 2015
Article copyright: © Copyright 2015 American Mathematical Society

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