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This article is cited in 22 scientific papers (total in 22 papers)
Complex-analytic structures on moment-angle manifolds
Taras Panovabc, Yuri Ustinovskya a Department of Mathematics and Mechanics, Moscow State University, Moscow, Russia,
b Institute for Information Transmission Problems, Russian Academy of Sciences
c Institute for Theoretical and Experimental Physics, Moscow, Russia,
Abstract:
We show that the moment-angle manifolds corresponding to complete simplicial fans admit non-Kähler 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.
Key words and phrases:
moment-angle manifold, simplicial fan, simple polytope, complex structure, Dolbeault cohomology, Hodge numbers.
Received: September 3, 2010; in revised form March 1, 2011
Citation:
Taras Panov, Yuri Ustinovsky, “Complex-analytic structures on moment-angle manifolds”, Mosc. Math. J., 12:1 (2012), 149–172
Linking options:
https://www.mathnet.ru/eng/mmj451 https://www.mathnet.ru/eng/mmj/v12/i1/p149
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Abstract page: | 459 | References: | 85 |
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