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

2005/08/04 by Yi Li, Li, Yi · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th #math.DG

paper · pdf · doi:10.48550/arxiv.hep-th/0508030

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

openalex publication_date 2005/08/04 · arxiv created 2005/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Generalized geometry and the Hodge decomposition
• Mirror Manifolds And Topological Field Theory
• Topological sigma-models with H-flux and twisted generalized complex manifolds
• Generalized Complex Geometry

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