论文标题
在Frobenius的Theta公式上
On Frobenius' theta formula
论文作者
论文摘要
芒福德（Mumford）在消失和非散落的theta常数方面对PPAV的模量空间的高纤维化基因座的众所周知的表征是基于Neumann的动力学系统的。穷人的表征方法使用了交叉比例。这两种方法中的一个关键工具是Frobenius的Theta公式，它遵循Riemann的Theta公式。在2004年的论文中，格鲁什夫斯基（Grushevsky）在二阶函数的立方方程方面给出了不同的表征。在本说明中，我们首先通过证明Grushevsky的立方方程与Frobenius的Theta公式有关，然后通过Gunning的多欧盟公式给出了amumford的表征的新证明，首先显示了方法之间的联系。
Mumford's well-known characterization of the hyperelliptic locus of the moduli space of ppavs in terms of vanishing and non-vanishing theta constants is based on Neumann's dynamical system. Poor's approach to the characterization uses the cross ratio. A key tool in both methods is Frobenius' theta formula, which follows from Riemann's theta formula. In a 2004 paper Grushevsky gives a different characterization in terms of cubic equations in second order theta functions. In this note we first show the connection between the methods by proving that Grushevsky's cubic equations are strictly related to Frobenius' theta formula and we then give a new proof of Mumford's characterization via Gunning's multisecant formula.
