Chapter

Complex and Differential Geometry

Volume 8 of the series Springer Proceedings in Mathematics pp 49-63

Date:

Holomorphic symplectic geometry: a problem list

  • Arnaud BeauvilleAffiliated withLaboratoire J.-A. Dieudonné (UMR 6621 du CNRS), Université de Nice Email author 

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Abstract

The usual structures of symplectic geometry (symplectic, contact, Poisson) make sense for complex manifolds; they turn out to be quite interesting on projective, or compact Kähler, manifolds. In these notes we review some of the recent results on the subject, with emphasis on the open problems and conjectures.

Keywords

symplectic contact Poisson manifolds hyperkähler manifolds Fujiki constant Lagrangian fibration quaternion-Kähler manifolds