Deformations of generalized complex and generalized Kahler structures
By R. Goto. 2007
73 citations recorded by the source corpus.
In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kahler manifolds which admits deformations to generalized complex manifolds and obtain non-trivial generalized Kahler structures on Fano surfaces and toric Kahler manifolds. In particular, we show that holomorphic Poisson structures on a Kahler manifold induce deformations of generalized Kahler structures.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/186ca955468689a1a6b339ea58fa9c34c4f70f09
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Branes on Poisson varieties (2007, methodology): “We therefore give an explicit construction of a subclass of the generalized Kähler structures proven to exist by the generalized Kähler stability theorem of Goto [4].”
- Generalized Kähler Geometry (2010, background): “This equivalence, obtained in the author’s thesis [23], was followed by a number of results, such as those contained in [8,10,17,19,22,24,29,30,32,35], which are not easily accessed purely from the bi-Hermitian point of view.”
- Deformations of holomorphic Poisson manifolds (2011, background): “We study in particular the Hilbert schemes of the projective plane and show that a generic deformation is determined by two parameters—an elliptic curve and a translation on it.”