On the discriminant of a hyperelliptic curve

The minimal discriminant of a hyperelliptic curve is defined and used to generalize much of the arithmetic theory of elliptic curves. Over number fields this leads to a higher genus version of Szpiro's Conjecture. Analytically, the discriminant is shown to be related to Siegel modular forms of higher degree.

超椭圆曲线的最小判别式被定义并用于推广椭圆曲线的许多算术理论。在数域上，这引出了斯皮罗猜想的高亏格版本。从分析角度来看，判别式被证明与更高次的西格尔模形式有关。