
ВИДЕОТЕКА 
Российскогерманская конференция по многомерному комплексному анализу



NonKähler complex structures on momentangle manifolds and other toric spaces Taras Panov^{} ^{} Moscow State University 

Аннотация: Momentangle complexes are spaces acted on by a torus and parameterised by finite simplicial complexes. They are central objects in toric topology, and currently are gaining much interest in homotopy theory. Due the their combinatorial origins, momentangle complexes also find applications in combinatorial geometry and commutative algebra. After an introductory part describing the general properties of momentangle complexes we shall concentrate on the complexanalytic aspects of the theory. We show that the momentangle manifolds corresponding to complete simplicial fans admit nonKähler complexanalytic structures. This generalises the known construction of complexanalytic structures on polytopal momentangle manifolds, coming from identifying them as LVMmanifolds (or nondegenerate intersections of Hermitian quadrics). The classical series of Hopf and Calabi–Eckmann manifolds are particular examples. We proceed by describing the Dolbeault cohomology and certain Hodge numbers of momentangle manifolds by applying the Borel spectral sequence to holomorphic principal bundles over toric varieties. (Joint work with Yuri Ustinovsky.) Язык доклада: английский 