Geometry of compact complex homogeneous spaces with vanishing first Chern class

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• 作者：Gueo Grantcharov^a ; ^{grantchg@fiu.edu}
• 关键词：Compact complex homogeneous spaces ; Hermitian connections ; Toric bundles ; Strominger's equations
• 刊名：Advances in Mathematics
• 出版年：2011
• 出版时间：1 March 2011
• 年：2011
• 卷：226
• 期：4
• 页码：3136-3159
• 全文大小：224 K

文摘

We prove that any compact complex homogeneous space with vanishing first Chern class, after an appropriate deformation of the complex structure, admits a homogeneous Calabi–Yau with torsion structure, provided that it also has an invariant volume form. A description of such spaces among the homogeneous C-spaces is given as well as many examples and a classification in the 3-dimensional case. We calculate the cohomology ring of some of the examples and show that in dimension 14 there are infinitely many simply-connected spaces admitting such a structure with the same Hodge numbers and torsional Chern classes. We provide also an example solving the Strominger's equations in heterotic string theory.