English

Local classification of generalized complex structures

Differential Geometry 2013-08-06 v4 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.1201.4887,
  title  = {Local classification of generalized complex structures},
  author = {Michael Bailey},
  journal= {arXiv preprint arXiv:1201.4887},
  year   = {2013}
}

Comments

29 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

R2 v1 2026-06-21T20:08:44.966Z