Generalized complex geometry encompasses complex and symplectic geometry as its
extremal special cases. We explore the basic properties of this geometry, including its …

The four-dimensional N= 1 supergravity theories arising in compactifications of type IIA and
type IIB on generalized orientifold backgrounds with background fluxes are discussed. The …

These lecture notes are based on a series of lectures given at the school on “Geometric and
Topological Methods for Quantum Field Theory”, in Villa de Leyva, Colombia. We present a …

A stable generalized complex structure is one that is generically symplectic but degenerates
along a real codimension two submanifold, where it defines a generalized Calabi–Yau …

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 …

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 …

We shall introduce the notion of C^ ∞ C∞ logarithmic symplectic structures on a
differentiable manifold which is an analog of the one of logarithmic symplectic structures in …

In this thesis we study geometric structures from Poisson and generalized complex geometry
with mild singular behavior using Lie algebroids. The process of lifting such structures to …

A generalized complex structure is called stable if its defining anticanonical section vanishes
transversally, on a codimension‐two submanifold. Alternatively, it is a zero elliptic residue …

In this note, four-manifold theory is employed to study generalized complex structures. We
drastically enlarge the number of available known examples of generalized complex four …