Deformations of nonsingular Poisson varieties and Poisson invertible sheaves

Chunghoon Kim

doi:10.1215/21562261-2019-0042

Abstract

We study deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend the flat deformation theory of nonsingular varieties and invertible sheaves. In the Appendix, we study deformations of Poisson vector bundles. We identify first-order deformations and obstructions.

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Chunghoon Kim. "Deformations of nonsingular Poisson varieties and Poisson invertible sheaves." Kyoto J. Math. 60 (2) 511 - 541, June 2020. https://doi.org/10.1215/21562261-2019-0042

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Received: 4 July 2016; Revised: 28 August 2017; Accepted: 1 December 2017; Published: June 2020

First available in Project Euclid: 22 February 2020

zbMATH: 07223243

MathSciNet: MR4094742

Digital Object Identifier: 10.1215/21562261-2019-0042

Subjects:

Primary: 14B10

Secondary: 14B12 , 17B63 , 32G07 , 53D17

Keywords: deformations of invertible sheaves , infinitesimal deformations of algebraic schemes , obstructions , Poisson cohomology , Poisson deformations , Poisson invertible sheaves , Poisson vector bundles

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