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- W3102166914 abstract "The first part of this paper is a generalization of the Feix-Kaledin theorem on the existence of a hyperkahler metric on a neighbourhood of the zero section of the cotangent bundle of a Kahler manifold. We show that the problem of constructing a hyperkahler structure on a neighbourhood of a complex Lagrangian submanifold in a holomorphic symplectic manifold reduces to the existence of certain deformations of holomorphic symplectic structures. The Feix-Kaledin structure is recovered from the twisted cotangent bundle. We then show that every holomorphic symplectic groupoid over a compact holomorphic Poisson surface of Kahler type has a hyperkahler structure on a neighbourhood of its identity section. More generally, we reduce the existence of a hyperkahler structure on a symplectic realization of a holomorphic Poisson manifold of any dimension to the existence of certain deformations of holomorphic Poisson structures adapted from Hitchin's unobstructedness theorem." @default.
- W3102166914 created "2020-11-23" @default.
- W3102166914 creator A5045991425 @default.
- W3102166914 date "2020-11-18" @default.
- W3102166914 modified "2023-09-27" @default.
- W3102166914 title "Hyperkahler metrics near Lagrangian submanifolds and symplectic groupoids" @default.
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