The group of Weierstrass points of a plane quartic with at least eight hyperflexes
The group of Weierstrass points of a plane quartic with at least eight hyperflexes
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具有至少八个超屈曲的平面四次方的 Weierstrass 点群
作者：
M. Girard
光滑曲线的魏尔斯特拉斯点在其雅可比矩阵中生成的群是该曲线的一个内在不变量。我们为所有具有八个或更多超弯曲的光滑四次曲线确定这一组。由于魏尔斯特拉斯点与曲线的模空间密切相关，作为应用，我们得到了亏格为3的曲线的模空间M3中具有固定数目的超曲的一般四次曲线的秩和挠部分的界.
The group generated by the Weierstrass points of a smooth curve in its Jacobian is an intrinsic invariant of the curve. We determine this group for all smooth quartics with eight hyperflexes or more. Since Weierstrass points are closely related to moduli spaces of curves, as an application, we get bounds on both the rank and the torsion part of this group for a generic quartic having a fixed number of hyperflexes in the moduli space M 3 of curves of genus 3.