Geometry of compact complex homogeneous spaces with vanishing first Chern class

Gueo Grantcharov

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arXiv · 0905.0040

Geometry of compact complex homogeneous spaces with vanishing first Chern class

Gueo Grantcharov

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Abstract

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 with the same Hodge numbers and torsional Chern classes admitting such structure. We provide also an example solving the Strominger's equations in heterotic string theory.

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Gueo Grantcharov. 2009-05-01. Geometry of compact complex homogeneous spaces with vanishing first Chern class. https://arxiv.org/abs/0905.0040

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