The moduli space of curves of genus two covering elliptic curves
暂无分享,去创建一个
We consider the moduli spaceSn of curvesC of genus 2 with the property:C has a “maximal” mapf of degreen to an elliptic curveE. Here, the term “maximal” means that the mapf∶C→E doesn't factor over an unramified cover ofE. By Torelli mapSn is viewed as a subset of the moduli spaceA2 of principally polarized abelian surfaces. On the other hand the Humbert surfaceHΔ of invariant Δ is defined as a subvariety ofA2(C), the set of C-valued points ofA2. The purpose of this paper is to releaseSn withHΔ.
[1] Friedrich Hirzebruch,et al. Hilbert modular surfaces , 1973 .
[2] Adolf Krazer,et al. Lehrbuch der Thetafunktionen , 1905 .
[3] G. B. Mathews,et al. Kummer's Quartic Surface , 1990 .
[4] R. Kuhn. Curves of genus 2 with split Jacobian , 1988 .
[5] Michael Rosen. Abelian Varieties over ℂ , 1986 .
[6] G. Humbert. Sur les fonctions abéliennes singulières , 1899 .