论文标题
在Prym地图上的循环覆盖物属的两条曲线
On the Prym map for cyclic covers of genus two curves
论文作者
论文摘要
Prym地图分配给曲线的每个覆盖层都有两极分化的Abelian品种。在二属曲线的未经循环覆盖层的情况下，我们表明Prym图被精确地涂在Bielliptic覆盖层的位置上。关键观察结果是，我们可以自然地与具有环状极化的Abelian表面覆盖，然后可以用Abelian表面上的部分的乘法来解释Prym映射的编纂。此外，我们给出了Ramanan的结果不同的证据，即两个属的属属的程度足够高，绝不是过度的。
The Prym map assigns to each covering of curves a polarized abelian variety. In the case of unramified cyclic covers of curves of genus two, we show that the Prym map is ramified precisely on the locus of bielliptic covers. The key observation is that we can naturally associate to such a cover an abelian surface with a cyclic polarization, and then the codifferential of the Prym map can be interpreted in terms of multiplication of sections on the abelian surface. Furthermore, we give a different proof of a result by Ramanan that a genus two cyclic cover of degree sufficiently high is never hyperelliptic.
