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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Deformations of holomorphic Lagrangian fibrations


Author: Justin Sawon
Journal: Proc. Amer. Math. Soc. 137 (2009), 279-285
MSC (2000): Primary 53C26, 14D06, 14J60
Published electronically: July 10, 2008
MathSciNet review: 2439451
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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.


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Additional Information

Justin Sawon
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523-1874
Email: sawon@math.colostate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09473-2
PII: S 0002-9939(08)09473-2
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.