Taras Panov, Yuri Ustinovsky, “Complex-analytic structures on moment-angle manifolds”, Mosc. Math. J., 2012, Volume 12, Number 1,Pages <nobr>149

This article is cited in 23 papers

Complex-analytic structures on moment-angle manifolds

Taras Panov^abc, Yuri Ustinovsky^a

^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.

MSC: 32J18, 32L05, 32Q55, 57R19, 14M25

Received: September 3, 2010; in revised form March 1, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-1-149-172