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Type: Journal article
Title: Picard group of isotropic realizations of twisted poisson manifolds
Author: Fok, C.
Citation: Journal of Geometric Mechanics, 2016; 8(2):179-197
Publisher: American Institute of Mathematical Sciences
Issue Date: 2016
ISSN: 1941-4889
Statement of
Chi-Kwong Fok
Abstract: Let B be a twisted Poisson manifold with a fixed tropical affine structure given by a period bundle P. In this paper, we study the classification of almost symplectically complete isotropic realizations (ASCIRs) over B in the spirit of [DD]. We construct a product among ASCIRs in analogy with tensor product of line bundles, thereby introducing the notion of the Picard group of B. We give descriptions of the Picard group in terms of exact sequences involving certain sheaf cohomology groups, and find that the ‘N´eron-Severi group’ is isomorphic to H(2) (B,P). An example of an ASCIR over a certain open subset of a compact Lie group is discussed.
Rights: Copyright © 2016 American Institute of Mathematical Sciences
RMID: 0030074275
DOI: 10.3934/jgm.2016003
Appears in Collections:Mathematical Sciences publications

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