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
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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.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