Generalized complex geometry
Differential Geometry
2007-05-23 v2 Algebraic Geometry
Symplectic Geometry
Abstract
Generalized complex geometry, introduced by Hitchin, 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.
Cite
@article{arxiv.math/0703298,
title = {Generalized complex geometry},
author = {Marco Gualtieri},
journal= {arXiv preprint arXiv:math/0703298},
year = {2007}
}
Comments
49 pages, refined from math.DG/0401221 and updated with new constructions, added references.