Complex-analytic structures on moment-angle manifolds
Complex Variables
2012-04-30 v3 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1008.4764,
title = {Complex-analytic structures on moment-angle manifolds},
author = {Taras Panov and Yuri Ustinovsky},
journal= {arXiv preprint arXiv:1008.4764},
year = {2012}
}
Comments
22 pages, LaTeX2e. Revisions in v3: the result describing the Dolbeault cohomology ring (Theorem 5.4) is now proved without assuming that the base is Kaehler, and the proof is simplified