论文标题
Haupt-重新审视了Kapovich定理
Haupt--Kapovich theorem revisited
论文作者
论文摘要
由M. Kapovich重新发现的O. Haupt定理，并以他的证明援引Ratner理论庆祝，描述了可拓扑定位的表面上的一组De Rham共同体学类别，在纯粹的拓扑术语中，可以通过某些各自的复杂结构在某些各自的复杂结构中实现。我们试图描述同样的配对和共同体学类别的三元，这可以由阿伯利亚的差异在某些复杂的结构中实现。这导致我们在曲线的代数几何形状中遇到了一些有趣的问题，并给出了对Teichmüller空间的意外局部描述。
A theorem of O. Haupt, rediscovered by M. Kapovich and celebrated by his proof invoking Ratner theory, describes the set of de Rham cohomology classes on a topological orientable surface, which can be realized by an abelian differential in some respective complex structure, in purely topological terms. We make an attempt to describe similarly pairs and triples of cohomology classes, which can be realized by abelian differentials in some complex structure. This leads us to some interesting problems in algebraic geometry of curves, and gives an unexpected local description of the Teichmüller space.
