论文标题
Lagrangian Submanifolds和Symphectic groupoids附近的Hyperkahler指标
Hyperkahler metrics near Lagrangian submanifolds and symplectic groupoids
论文作者
论文摘要
本文的第一部分是Feix-kaledin定理的概括，内容涉及Hyperkahler指标在Kahler歧管的Cotangent Bundle的零部分的附近存在。我们表明，在全体形态的符号歧管中，在复杂的拉格朗日亚曼叶族附近构建超卡勒结构的问题减少了霍明型符号结构的某些变形的存在。从扭曲的cotangent束中恢复了Feix-Kaledin结构。然后，我们表明，卡勒类型的紧凑型全态泊松表面上的每个全态符号型组素在其身份部分的附近都具有Hyperkahler结构。更笼统地，我们减少了Hyperkahler结构的存在，以实现所有维度的全态Poisson歧管的象征性实现，从而存在着由Hitchin的Unobstructentness theorem定理所适应的Holomorthic Poisson结构的某些变形的存在。
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.
