9 citations · 32 across the 9 of their papers we have counts for
10 papers
A neighbourhood theorem for submanifolds in generalized complex geometry
Michael Bailey, Gil R. Cavalcanti, Joey van der Leer Duran
We study neighbourhoods of submanifolds in generalized complex geometry. Our first main result provides sufficient criteria for such a submanifold to admit a neighbourhood on which…
The local structure of generalized complex branes
Michael Bailey
We show (modulo a parity condition) that, a generalized complex brane in a generalized complex manifold is locally equivalent to a holomorphic coisotropic submanifold of a holomorp…
Integration of generalized complex structures
Michael Bailey, Marco Gualtieri
We solve the integration problem for generalized complex manifolds, obtaining as the natural integrating object a weakly holomorphic symplectic groupoid, which is a real symplectic…
Type one generalized Calabi--Yaus
Michael Bailey, Gil R. Cavalcanti, Marco Gualtieri
We study type one generalized complex and generalized Calabi--Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which…
Blow-ups in generalized complex geometry
Michael Bailey, Gil R. Cavalcanti, Joey van der Leer Duran
We study blow-ups in generalized complex geometry. To that end we introduce the concept of holomorphic ideal, which allows one to define a blow-up in the category of smooth manifol…
Local analytic geometry of generalized complex structures
Michael Bailey, Marco Gualtieri
A generalized complex manifold is locally gauge-equivalent to the product of a holomorphic Poisson manifold with a real symplectic manifold, but in possibly many different ways. In…
From locally conformally Kähler to bi-Hermitian structures on non-Kähler complex surfaces
Vestislav Apostolov, Michael Bailey, Georges Dloussky
We prove that locally conformally Kähler metrics on certain compact complex surfaces with odd first Betti number can be deformed to new examples of bi-Hermitian metrics.
Symplectic foliations and generalized complex structures
Michael Bailey
We answer the natural question: when are a regular Poisson structure along with a complex structure transverse to its symplectic leaves induced by generalized complex structure? Th…
On the local and global classification of generalized complex structures
Michael Bailey
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifo…
Local classification of generalized complex structures
Michael Bailey
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 holomorp…