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東工大 幾何セミナー: Nicholas Lindsay 氏

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日程
2020年7月17日(金)
時間
16:30~18:00
場所
Zoomによる開催 
講師
Nicholas Lindsay 氏(上海科技大学)
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講演タイトル
Hamiltonian group actions and non-Kahler symplectic structures.
アブストラクト
 There are many examples of symplectic manifolds which cannot have a Kahler structure. However, in the presence of a Hamiltonian torus action, such examples are more scarce. For example Delzant proved that if there is a Hamiltonian action of a half dimensional torus then the symplectic manifold is necessarily Kahler. Also, Karshon proved that the existence of a Hamiltonian circle action on a closed symplectic 4-manifold, implies the manifold is Kahler. For a long time, it was unknown whether a closed symplectic manifold with a Hamiltonian torus action with finite fixed point set has an invariant Kahler metric. Then, Tolman constructed a closed symplectic 6-manifold with a Hamiltonian T^2-action with 6 fixed points not having a T^2-invariant Kahler metric.

 Recently, Goertsches, Konstantis and Zoller shows that Tolmans manifold is diffeomorphic to a projective bundle over CP^2, hence has some Kahler metric. I will discuss a joint work with Dmitri Panov, in which we showed that the symplectic form constructed by Tolman has no compatible Kahler metric. The settles the problem of finding a compact symplectic manifold with a Hamiltonian circle action with finite fixed point set not having a compatible Kahler metric.
 

更新日:2020.07.08

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