Local classification of generalized complex structures

Abstract

We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn's linearization theorem.

arXiv comment29 pages, adapted from Ph.D. thesis; v2 changes: retitled, shortened abstract, corrected typos, changed formatting; v3 changes: equation (2.9) was missing a term, proof of Lemma 6.9 adjusted to accommodate; v4 changes: slight editing, closer to published version

References in corpus (6)

• Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
• A surgery for generalized complex structures on 4-manifolds
• Blow-up of generalized complex 4-manifolds
• Rigidity of Hamiltonian actions on Poisson manifolds
• Normal forms in Poisson geometry
• On the local and global classification of generalized complex structures

Cited by in corpus (4)

• Poisson modules and degeneracy loci
• Stable generalized complex structures
• The Local Structure of Generalized Contact Bundles
• Generalized twistor spaces for hyperkähler manifolds