English

Blow-up of generalized complex 4-manifolds

Symplectic Geometry 2013-08-20 v2 High Energy Physics - Theory Differential Geometry

Abstract

We introduce blow-up and blow-down operations for generalized complex 4-manifolds. Combining these with a surgery analogous to the logarithmic transform, we then construct generalized complex structures on nCP2 # m \bar{CP2} for n odd, a family of 4-manifolds which admit neither complex nor symplectic structures unless n=1. We also extend the notion of a symplectic elliptic Lefschetz fibration, so that it expresses a generalized complex 4-manifold as a fibration over a two-dimensional manifold with boundary.

Keywords

Cite

@article{arxiv.0806.0872,
  title  = {Blow-up of generalized complex 4-manifolds},
  author = {Gil R. Cavalcanti and Marco Gualtieri},
  journal= {arXiv preprint arXiv:0806.0872},
  year   = {2013}
}

Comments

25 pages, 15 figures. This is the final version, which was published in J. Top

R2 v1 2026-06-21T10:47:38.369Z