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The Many Facets of GeometryA Tribute to Nigel Hitchin$
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Oscar Garcia-Prada, Jean Pierre Bourguignon, and Simon Salamon

Print publication date: 2010

Print ISBN-13: 9780199534920

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199534920.001.0001

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Branes on Poisson Varieties

Branes on Poisson Varieties

(p.368) XVIII Branes on Poisson Varieties
The Many Facets of Geometry

Marco Gualtieri

Oxford University Press

This chapter takes a second look at a classical structure in differential and algebraic geometry — that of a holomorphic Poisson structure — which is a complex manifold with a holomorphic Poisson bracket on its sheaf of regular functions. The structure is determined, on a real smooth manifold M, by the choice of a pair (I, δI), where I is an integrable complex structure tensor and δI is a holomorphic Poisson tensor. (I, δI) is viewed as a generalized complex structure, in the sense of Hitchin. In viewing it in this way, the chapter provides a new notion of equivalence between the pairs (I, δI) which does not imply the holomorphic equivalence of the underlying complex structures.

Keywords:   holomorphic Poisson structure, complex manifold, Poisson bracket, smooth manifold

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