Generalized complex geometry

Pages 75-123 from Volume 174 (2011), Issue 1 by Marco Gualtieri

Abstract

Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds.

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DOI
http://doi.org/10.4007/annals.2011.174.1.3
MR
2811595
zbMATH
05960697
Milestones
Received: 1 April 2007
Revised: 19 November 2009
Accepted: 11 June 2010
Published online: 1 July 2011

Authors

Marco Gualtieri

Department of Mathematics
University of Toronto
Toronto, Ontario
Canada M5S 2E4