Complex compact manifolds with maximal torus action

Complex compact manifolds with maximal torus action

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Yury Ustinovsky, Moscow State University
Fine Hall 401

Please note different time and location.  In the talk we describe a class of manifolds Z 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 and a C*-torus action transitive in the transverse direction. Examples of moment-angle manifolds include Hopf manifolds of Vaisman type, Calabi-Eckmann manifolds, and their deformations.   Recent results of H. Ishida imply that these manifolds are the only compact complex manifolds with maximal torus action. Explicit construction of the manifold allows precise description of its geometry and topology e.g. Hodge numbers, cohomology ring, complex submanifolds. http://arxiv.org/abs/1308.2818 T.Panov, Y.Ustinovskiy, M.Verbitsky http://arxiv.org/abs/1302.0633 H.Ishida http://arxiv.org/abs/1008.4764T.Panov, Y.Ustinovskiy