论文标题
球商参数化三角属4曲线
A ball quotient parametrizing trigonal genus 4 curves
论文作者
论文摘要
我们考虑了带有$ g^1_3 $的属4曲线的模量空间（该曲线映射为2曲线4曲线的模量空间）。我们证明，它定义了$ \ frac {1} {2}（3^{10} -1）$的9维deligne-mostow球商的封面，使得生活在Moduli空间上的自然除数变得完全地理位置（它们的正常化是8维球的标准）。 这种同构不同于S.Kondō所考虑的同构及其构建可能更基本，因为它不涉及K3表面及其Torelli定理：Deligne-Mostow-Mostow Ball商参数参数参数一定的一定程度覆盖了一个投影线的6度覆盖范围的某些环环，我们显示了与该级别覆盖的一流范围相同的一流的一流的层面，该级别的结构是一定的。 $ g^1_3 $。
We consider the moduli space of genus 4 curves endowed with a $g^1_3$ (which maps with degree 2 onto the moduli space of genus 4 curves). We prove that it defines a degree $\frac{1}{2}(3^{10}-1)$ cover of the 9-dimensional Deligne-Mostow ball quotient such that the natural divisors that live on that moduli space become totally geodesic (their normalizations are 8-dimensional ball quotients). This isomorphism differs from the one considered by S. Kondō and its construction is perhaps more elementary, as it does not involve K3 surfaces and their Torelli theorem: the Deligne-Mostow ball quotient parametrizes certain cyclic covers of degree 6 of a projective line and we show how a level structure on such a cover produces a degree 3 cover of that line with the same discriminant, yielding a genus 4 curve endowed with a $g^1_3$.
