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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Fibered stable varieties
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by Zsolt Patakfalvi PDF
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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Additional Information
  • Zsolt Patakfalvi
  • Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
  • Email: pzs@math.princeton.edu
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 1837-1869
  • MSC (2010): Primary 14J10; Secondary 14J40
  • DOI: https://doi.org/10.1090/tran/6386
  • MathSciNet review: 3449226