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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Deformations of holomorphic Lagrangian fibrations
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by Justin Sawon
Proc. Amer. Math. Soc. 137 (2009), 279-285
DOI: https://doi.org/10.1090/S0002-9939-08-09473-2
Published electronically: July 10, 2008

Abstract:

Let $X\rightarrow \mathbb {P}^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $\mathbb {P}^n$. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space $\mathrm {Def}(X)$ of deformations of $X$. We extend his result by proving that if the Lagrangian fibration admits a section, then there is a codimension two family of deformations which also preserve the section.
References
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Bibliographic Information
  • Justin Sawon
  • Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523-1874
  • MR Author ID: 653333
  • Email: sawon@math.colostate.edu
  • Received by editor(s): October 12, 2006
  • Received by editor(s) in revised form: March 2, 2007, and December 31, 2007
  • Published electronically: July 10, 2008
  • Communicated by: Ted Chinburg
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 279-285
  • MSC (2000): Primary 53C26, 14D06, 14J60
  • DOI: https://doi.org/10.1090/S0002-9939-08-09473-2
  • MathSciNet review: 2439451