Singular Reduction of Generalized Complex Manifolds

Details Singular Reduction of Generalized Complex Manifolds Singular Reduction of Generalized Complex Manifolds

2010-03-09

arxiv.org/abs/1003.1773v4

SIGMA 6 (2010), 081, 17 pages

Mathematics

Differential Geometry

v3: narrative streamlined and typos corrected from original version; v4: published version

Scientific paper

10.3842/SIGMA.2010.081

In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin and Tolman). Specifically, we prove that if a compact Lie group acts on a generalized complex manifold in a Hamiltonian fashion, then the partition of the global quotient by orbit types induces a partition of the Lin-Tolman quotient into generalized complex manifolds. This result holds also for reduction of Hamiltonian generalized K\"ahler manifolds.

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