Blowup of generalized complex 4manifolds
Abstract
We introduce blowup and blowdown operations for generalized complex 4manifolds. 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 4manifolds 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 4manifold as a fibration over a twodimensional manifold with boundary.
 Publication:

arXiv eprints
 Pub Date:
 June 2008
 DOI:
 10.48550/arXiv.0806.0872
 arXiv:
 arXiv:0806.0872
 Bibcode:
 2008arXiv0806.0872C
 Keywords:

 Mathematics  Symplectic Geometry;
 High Energy Physics  Theory;
 Mathematics  Differential Geometry;
 53C15;
 53D05;
 14E05
 EPrint:
 25 pages, 15 figures. This is the final version, which was published in J. Top