Generalized complex geometry and blow-ups

Abstract

Blowing up is a well-known procedure to resolve singularities and create new spaces with certain kinds of geometric structures. Although the technique of blowing-up is well studied in all kinds of categories, in generalized complex and generalized Kähler geometry the only known results are in dimension 4. In my thesis we study the higher dimensions and find some partial results on lifting the generalized complex and generalized Kähler structure to the blown-up manifold.