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LAGRANGIAN FIBRATIONS OF HYPERKÄHLER FOURFOLDS

Published online by Cambridge University Press:  20 July 2020

Daniel Huybrechts Open the ORCID record for Daniel Huybrechts [Opens in a new window]  and
Chenyang Xu
Daniel Huybrechts
Affiliation:
Mathematisches Institut and Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (huybrech@math.uni-bonn.de)
Chenyang Xu
Affiliation:
Mathematics Department, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA (cyxu@mit.edu) BICMR, Beijing, China (cyxu@math.pku.edu.cn)
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Abstract

The base surface $B$ of a Lagrangian fibration of a projective, irreducible symplectic fourfold $X$ is shown to be isomorphic to $\mathbb{P}^{2}$.

Keywords

Lagrangian fibrationsirreducible symplectic varietieshyperkähler manifolds

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 3 , May 2022 , pp. 921 - 932
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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Footnotes

DH is supported by the SFB/TR 45 ‘Periods, Moduli Spaces and Arithmetic of Algebraic Varieties’ of the DFG (German Research Foundation). CX is partially supported by a Chern Professorship of the MSRI (NSF No. DMS-1440140) and by the National Science Fund for Distinguished Young Scholars (NSFC 11425101) ‘Algebraic Geometry’.

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