Geometry Colloquium

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Date, time & place Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.)

2012/12/05

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroaki Ishida (Osaka City University Advanced Mathematical Institute)
Maximal torus actions on complex manifolds (JAPANESE)
[ Abstract ]
We say that an effective action of a compact torus $T$ on a connected manifold $M$ is maximal if there is an orbit of dimension $2\\dim T-\\dim M$. In this talk, we give a one-to-one correspondence between the family of connected closed complex manifolds with maximal torus actions and the family of certain combinatorial objects, which is a generalization of the correspondence between complete nonsingular toric varieties and nonsingular complete fans. As an application, we construct a lot of concrete examples of non-K\\"{a}hler manifolds with maximal torus actions.