Deformation in holomorphic Poisson manifolds

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)277-286
Number of pages10
JournalDifferential Geometry and its Application
Volume49
DOIs
StatePublished - Dec 1 2016

Fingerprint

Poisson Manifolds
Algebra
Submanifolds
Poisson Structure

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

Cite this

@article{9d9e1406ac1a4c0189de26af7cad261e,
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",
year = "2016",
month = "12",
day = "1",
doi = "10.1016/j.difgeo.2016.08.007",
language = "English (US)",
volume = "49",
pages = "277--286",
journal = "Differential Geometry and its Applications",
issn = "0926-2245",
publisher = "Elsevier",

}

Deformation in holomorphic Poisson manifolds. / Ji, Xiang.

In: Differential Geometry and its Application, Vol. 49, 01.12.2016, p. 277-286.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Deformation in holomorphic Poisson manifolds

AU - Ji, Xiang

PY - 2016/12/1

Y1 - 2016/12/1

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.

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

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

U2 - 10.1016/j.difgeo.2016.08.007

DO - 10.1016/j.difgeo.2016.08.007

M3 - Article

VL - 49

SP - 277

EP - 286

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

SN - 0926-2245

ER -