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Moscow Mathematical Journal, 2012, Volume 12, Number 1, Pages 149–172
DOI: https://doi.org/10.17323/1609-4514-2012-12-1-149-172 (Mi mmj451) 		 
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,
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DOI: https://doi.org/10.17323/1609-4514-2012-12-1-149-172
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
Bibliographic databases:
Document Type: Article
MSC: 32J18, 32L05, 32Q55, 57R19, 14M25
Language: English
Citation: Taras Panov, Yuri Ustinovsky, “Complex-analytic structures on moment-angle manifolds”, Mosc. Math. J., 12:1 (2012), 149–172
Citation in format AMSBIB
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\by Taras~Panov, Yuri~Ustinovsky
\paper Complex-analytic structures on moment-angle manifolds
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 149--172
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\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-149-172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2952429}
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