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Complex geometry of moment-angle manifolds
Mathematische Zeitschrift. 2016. Vol. 284. No. 1. P. 309–333.
Panov T., Ustinovskiy Y., Verbitsky M.
Moment-angle manifolds provide a wide class of examples of non-Kähler compact complex manifolds. A complex moment-angle manifold ZZis zero.
Keywords: holomorphic foliationsMoment-angle manifoldNon-Kähler complex structureSimplicial fanTransversely Kähler metric
Publication based on the results of:
Panov T., Bulletin of the London Mathematical Society 2025 Vol. 57 No. 9 P. 2571–2629
Exponential actions defined by vector configurations provide a universal framework for several constructions of holomorphic dynamics, non-Kähler complex geometry, toric geometry and topology. These include leaf spaces of holomorphic foliations, intersections of real and Hermitian quadrics, the quotient construction of simplicial toric varieties, LVM and LVMB manifolds, complex-analytic structures on moment-angle manifolds and their partial ...
Added: August 5, 2025
Aleksei Golota, Mathematische Nachrichten 2023 Vol. 296 No. 11 P. 5012–5029
The aim of this paper is to classify codimension 1 foliations ℱ with canonical
singularities and 𝜈(𝐾 ℱ ) < 3 on threefolds of general type. I prove a classification
result for foliations satisfying these conditions and having nontrivial algebraic
part. We also describe purely transcendental foliations ℱ with the canonical class
𝐾 ℱ being not big on manifolds ...
Added: September 4, 2023
Ishida H., Krutowski R., Panov T., International Mathematics Research Notices 2022 Vol. 2022 No. 7 P. 5541–5563
We describe the basic cohomology ring of the canonical holomorphic foliation on a moment-angle manifold, LVMB-manifold, or any complex manifold with a maximal holomorphic torus action. Namely, we show that the basic cohomology has a description similar to the cohomology ring of a complete simplicial toric variety due to Danilov and Jurkiewicz. This settles a ...
Added: October 29, 2021
Krutowski R., Panov T., Contemporary Mathematics 2021 Vol. 772 P. 173–187
We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality, complex manifolds with a maximal holomorphic torus action. We also provide a dga model for the ordinary Dolbeault cohomology algebra. ...
Added: October 27, 2021
Limonchenko I., Математические заметки 2013 Т. 94 № 3 С. 373–388
We calculate certain bigraded Betti numbers for associahedra and apply the calculation of bigraded Betti numbers for truncation polytopes to study the topology of their moment-angle manifolds. Presumably, for these two series of simple polytopes, the bigraded Betti numbers attain their minimum and maximum values among all simple polytopes of fixed dimension with a given ...
Added: September 29, 2019
Limonchenko I., Труды Математического института им. В.А. Стеклова РАН 2014 Т. 286 С. 207–218
We consider simple polytopes that are vertex cuts of products of simplices, and call them generalized truncation polytopes. For these polytopes we describe the cohomology ring of the corresponding moment–angle manifold and explore some topological consequences of this calculation. We also examine minimal non-Golodness for their Stanley–Reisner rings and relate it to the property of a moment-angle ...
Added: September 29, 2019
Limonchenko I., Успехи математических наук 2016 Т. 71 № 2 С. 207–208
We give the first example of polyhedral products with nontrivial higher Massey products of any prescribed order in cohomology. ...
Added: September 29, 2019
Campana F., Demailly J., Verbitsky M., Algebraic Geometry 2014 Vol. 2 P. 131–139
We prove that any compact Kahler 3-dimensional manifold which has no nontrivial complex subvarieties is a torus. This is a very special case of a general conjecture on the structure of so-called simple manifolds, central in the bimeromorphic classi cation of compact Kahler manifolds. The proof follows from the Brunella pseudo-e ectivity theorem, combined with fundamental results ...
Added: April 29, 2014