Gardado en:
| Autor Principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2011.09282 |
| Tags: |
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Table of Contents:
- 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.