论文标题
平坦表面的模量空间
Volumes of moduli spaces of flat surfaces
论文作者
论文摘要
我们研究具有规定的圆锥形奇异性的平面平面的模量空间。 Veech表明，这些空间与标记的Riemann表面的模量空间具有差异性，并根据奇异性的顺序赋予自然体积形式。我们表明这些空间的量是有限的。此外，我们表明，对于几乎所有奇异性的顺序，它们都可以通过对刺穿表面的Euler特征诱导明确计算。
We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the orders of the singularities. We show that the volumes of these spaces are finite. Moreover we show that they are explicitely computable by induction on the Euler characteristics of the punctured surface for almost all orders of the singularities.
