Complex-analytic structures on moment-angle manifolds

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.

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

References in corpus (1)

• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces

Cited by in corpus (4)

• Moment-angle manifolds and complexes. Lecture notes KAIST'2010
• Dolbeault cohomology of complex manifolds with torus action
• Exponential actions defined by vector configurations, Gale duality, and moment-angle manifolds
• Gale transform of a starshaped sphere