On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case

Abstract

We prove an analog of the Tian-Todorov theorem for twisted generalized Calabi-Yau manifolds; namely, we show that the moduli space of generalized complex structures on a compact twisted generalized Calabi-Yau manifold is unobstructed and smooth. We also construct the extended moduli space and study its Frobenius structure. The physical implications are also discussed.

28 pages; typos corrected; Lemma 2 slightly generalized and one appendix added

References in corpus (9)

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Cited by in corpus (22)

• Lectures on Generalized Complex Geometry for Physicists
• Deformations of calibrated D-branes in flux generalized complex manifolds
• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• On moduli and effective theory of N=1 warped flux compactifications
• The Hitchin functionals and the topological B-model at one loop
• Lectures on Generalized Complex Geometry and Supersymmetry
• Poisson sigma model on the sphere
• T-duality and Generalized Kahler Geometry
• The biHermitian topological sigma model
• Extension formulas and deformation invariance of Hodge numbers
• Formality in generalized Kahler geometry
• Twisted Analytic Torsion
• On deformations of generalized Calabi-Yau, hyperKähler, $G_2$ and Spin$(7)$ structures I
• Power series proofs for local stabilities of Kähler and balanced structures with mild $\partial \bar{\partial }$-lemma
• The minimal model for the Batalin-Vilkovisky operad
• Generalized Almost Product Structures and Generalized CRF-structures
• Several special complex structures and their deformation properties
• On special geometry of the moduli space of string vacua with fluxes
• Remarks on the Cartan Formula and Its Applications
• Extensions of $\overline{\partial }$-closed forms on compact generalized Hermitian manifolds
• Some Results of Deformations on Compact $H$-twisted Generalized Calabi-Yau Manifolds
• On Tian-Todorov lemma and its applications to deformation of CR-structures