Geometry and Physics: Volume II - A Festschrift in honour of Nigel Hitchin
Geometry and Physics: Volume II - A Festschrift in honour of Nigel Hitchin
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几何与物理：第二卷 - 纪念奈杰尔·希钦的纪念文集
DOI：
10.1093/oso/9780198802020.003.0028
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Pym B
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文献类型：
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作者：
Pym B
我们介绍了一个自然的非退化条件的泊松结构，称为holonomicity，这是密切相关的概念的对数辛形式。完整泊松流形的特权在于它们的变形空间是有限维的，正如人们所希望的那样：相应的导出的变形复形是一个反常层。我们开发了这些流形的一些基本结构特征，突出了哈密顿向量场的发散所发挥的作用。作为应用，我们建立了由Feigin和Odesskii定义的Poisson流形的某些族的形变不变性，沿着的“椭圆代数”，包围他们。
We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manifolds are privileged by the fact that their deformation spaces are as finite-dimensional as one could ever hope: the corresponding derived deformation complex is a perverse sheaf. We develop some basic structural features of these manifolds, highlighting the role played by the divergence of Hamiltonian vector fields. As an application, we establish the deformation-invariance of certain families of Poisson manifolds defined by Feigin and Odesskii, along with the "elliptic algebras" that quantize them.