255 citations · 926 across the 27 of their papers we have counts for
20 papers · 1 filter
Symplectic double groupoids and the generalized Kähler potential
Daniel Álvarez, Marco Gualtieri, Yucong Jiang
A description of the fundamental degrees of freedom underlying generalized Kähler geometry, which separates its holomorphic moduli from its compatible Riemannian metric in a simila…
Brane quantization of toric Poisson varieties
Francis Bischoff, Marco Gualtieri
In this paper we propose a noncommutative generalization of the relationship between compact Kähler manifolds and complex projective algebraic varieties. Beginning with a prequanti…
Generalized Kähler metrics from Hamiltonian deformations
Marco Gualtieri
We give a new characterization of generalized Kähler structures in terms of their corresponding complex Dirac structures. We then give an alternative proof of Hitchin's partial uno…
Morita equivalence and the generalized Kähler potential
Francis Bischoff, Marco Gualtieri, Maxim Zabzine
We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kähler structure of symplectic type. For a usual Kähler structure, it is well-known…
Deformation of Dirac structures via algebras
M. Gualtieri, M. Matviichuk, G. Scott
The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra which depends on the choice of an auxiliary transversal Dirac structure; if the trans…
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…
Stable generalized complex structures
Gil R. Cavalcanti, Marco Gualtieri
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 str…
Generalized Kaehler geometry of instanton moduli spaces
Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri
We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehle…
Generalized complex geometry and T-duality
Gil R. Cavalcanti, Marco Gualtieri
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories di…
Blowing up generalized Kahler 4-manifolds
Gil R. Cavalcanti, Marco Gualtieri
We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metri…
Generalized Kahler geometry
Marco Gualtieri
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible…
Branes on Poisson varieties
Marco Gualtieri
We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of is…
Generalized complex geometry
Marco Gualtieri
Generalized complex geometry, introduced by Hitchin, encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, in…
Generalized Kahler and hyper-Kahler quotients
Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri
We develop a theory of reduction for generalized Kahler and hyper-Kahler structures which uses the generalized Riemannian metric in an essential way, and which is not described wit…
Generalized Kaehler manifolds with split tangent bundle
Vestislav Apostolov, Marco Gualtieri
We study generalized Kaehler manifolds for which the corresponding complex structures commute and classify completely the compact generalized Kaehler four-manifolds for which the i…
A surgery for generalized complex structures on 4-manifolds
Gil R. Cavalcanti, Marco Gualtieri
We introduce a surgery for generalized complex manifolds whose input is a symplectic 4-manifold containing a symplectic 2-torus with trivial normal bundle and whose output is a 4-m…
Reduction of Courant algebroids and generalized complex structures
Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri
We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic r…
Generalized geometry and the Hodge decomposition
Marco Gualtieri
In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the…
Generalized complex structures on nilmanifolds
Gil R. Cavalcanti, Marco Gualtieri
We show that all 6-dimensional nilmanifolds admit generalized complex structures. This includes the five classes of nilmanifold which admit no known complex or symplectic structure…
Generalized complex geometry
Marco Gualtieri
Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited…