Complex-analytic structures on moment-angle manifolds

Details Complex-analytic structures on moment-angle manifolds Complex-analytic structures on moment-angle manifolds

2010-08-27

arxiv.org/abs/1008.4764v2

Mathematics

Complex Variables

22 pages, LaTeX2e. Revisions in v2: (a) new references and credits added; (b) the argument for the properness of the action in

Scientific paper

We show that the moment-angle manifolds corresponding to complete simplicial fans admit non-Kaehler complex-analytic structures. This generalises the known construction of complex-analytic structures on polytopal moment-angle manifolds, coming from identifying them as LVM-manifolds. We proceed by describing Dolbeault cohomology and some Hodge numbers of moment-angle manifolds by applying the Borel spectral sequence to holomorphic principal bundles over toric varieties.

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