Deformation in holomorphic Poisson manifolds

Xiang Ji

doi:10.1016/j.difgeo.2016.08.007

Deformation in holomorphic Poisson manifolds

Xiang Ji

Penn State New Kensington

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold (X,π). Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an L_∞-algebra that controls the deformations of Y. This L_∞-algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y.

Original language	English (US)
Pages (from-to)	277-286
Number of pages	10
Journal	Differential Geometry and its Application
Volume	49
DOIs	https://doi.org/10.1016/j.difgeo.2016.08.007
State	Published - Dec 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology
Computational Theory and Mathematics

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10.1016/j.difgeo.2016.08.007

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title = "Deformation in holomorphic Poisson manifolds",

abstract = "In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold (X,π). Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an L∞-algebra that controls the deformations of Y. This L∞-algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y.",

author = "Xiang Ji",

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doi = "10.1016/j.difgeo.2016.08.007",

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AU - Ji, Xiang

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N2 - In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold (X,π). Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an L∞-algebra that controls the deformations of Y. This L∞-algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y.

AB - In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold (X,π). Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an L∞-algebra that controls the deformations of Y. This L∞-algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y.

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UR - https://www.scopus.com/inward/citedby.url?scp=84986563078&partnerID=8YFLogxK

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DO - 10.1016/j.difgeo.2016.08.007

M3 - Article

AN - SCOPUS:84986563078

SN - 0926-2245

VL - 49

SP - 277

EP - 286

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

Deformation in holomorphic Poisson manifolds

Abstract

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