ON THE SYMPLECTIC STRUCTURE OVER A MODULI SPACE OF ORBIFOLD PROJECTIVE STRUCTURES
ON THE SYMPLECTIC STRUCTURE OVER A MODULI SPACE OF ORBIFOLD PROJECTIVE STRUCTURES
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论轨道折叠射影结构模空间上的辛结构
DOI：
10.4310/jsg.2017.v15.n3.a1
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
I. Biswas
中科院分区：
文献类型：
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作者：
Pablo Arés;I. Biswas
设S是紧连通定向orbifold曲面，利用Bers同时一致化，证明了S上投射结构的模空间可以双全纯映射到S的Teichmuller空间的全纯余切丛的全空间上. Teichm uller空间的全纯余切丛的全空间具有Liouville辛形式，射影结构的模空间也具有自然的全纯辛形式.证明了上述识别与这些辛结构是相容的。类似的结果得到了双全纯构造使用由肖特基群和厄尔的版本的同时均匀化提供的均匀化。
Let S be a compact connected oriented orbifold surface We show that using Bers simultaneous uniformization, the moduli space of projective structure on S can be mapped biholomorphically onto the total space of the holomorphic cotangent bundle of the Teichm\"uller space for S. The total space of the holomorphic cotangent bundle of the Teichm\"uller space is equipped with the Liouville symplectic form, and the moduli space of projective structures also has a natural holomorphic symplectic form. The above identification is proved to be compatible with these symplectic structures. Similar results are obtained for biholomorphisms constructed using uniformizations provided by Schottky groups and Earle's version of simultaneous uniformization.