Complex geometry of moment-angle manifolds

Панов, Т.Е.; Устиновский, Ю.М.; Вербицкий, М.С.

Авторы: Панов Тарас Евгеньевич, Устиновский Юрий Михайлович, Вербицкий Михаил Сергеевич
Журнал: Mathematische Zeitschrift
Том: 284
Номер: 1
Год издания: 2016
Издательство: Springer Verlag
Местоположение издательства: Germany
Первая страница: 309
Последняя страница: 333
DOI: 10.1007/s00209-016-1658-1
Аннотация: Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variety with fibres compact complex tori. In general, a complex moment-angle manifold Z is equipped with a canonical holomorphic foliation F which is equivariant with respect to the (C*)^m-action. Examples of moment-angle manifolds include Hopf manifolds of Vaisman type, Calabi-Eckmann manifolds, and their deformations. We construct transversely Kaehler metrics on moment-angle manifolds, under some restriction on the combinatorial data. We prove that any Kaehler submanifold (or, more generally, a Fujiki class C subvariety) in such a moment-angle manifold is contained in a leaf of the foliation F. For a generic moment-angle manifold Z in its combinatorial class, we prove that all subvarieties are moment-angle manifolds of smaller dimension. This implies, in particular, that the algebraic dimension of Z is zero.
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Complex geometry of moment-angle manifoldsстатья

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