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Blow-up of generalized complex 4-manifolds

By Gil R. Cavalcanti and Marco Gualtieri

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 nCP 2 #mCP 2 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

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