论文标题
在Galois覆盖的Prym地图上
On the Prym map of Galois covering
论文作者
论文摘要
在本文中，我们考虑prym varivent $ p（\ widetilde {c}/c）$与曲线的Galois覆盖物相关的$ f：\ widetilde {c} \ to c $ r $ $点分支。我们讨论了一些属性和等效定义，然后考虑prym映射$ \ MATHCAL {p} = \ MATHCAL {p}（g，g，g，r）：r（g，g，g，r）\ to a_ {p，Δ} $，带有$Δ$ $Δ$ $ upallization的类型。对于Galois组为Abelian和Metabelian（非亚伯利亚）的Galois覆盖物，我们表明该地图在某些点的差异是注入性的。我们还将Abel-Prym Map $ u：\ widetilde {c} \ to p（\ widetilde {c}/c）$，并证明其注射率得到了一些结果。特别是我们表明，与经典和循环案例相反，此地图的行为更为复杂。阿贝利亚和Metabelian Galois覆盖物的理论在我们的分析中起着重要作用，并且在整个论文中已被广泛使用。
In this paper we consider the Prym variety $P(\widetilde{C}/C)$ associated to a Galois coverings of curves $f:\widetilde{C}\to C$ branched at $r$ points. We discuss some properties and equivalent definitions and then consider the Prym map $\mathcal{P}=\mathcal{P}(G,g,r):R(G,g,r)\to A_{p,δ}$ with $δ$ the type of the polarization. For Galois coverings whose Galois group is abelian and metabelian (non-abelian) we show that the differential of this map at certain points is injective. We also consider the Abel-Prym map $u:\widetilde{C}\to P(\widetilde{C}/C)$ and prove some results for its injectivity. In particular we show that in contrast to the classical and cyclic case, the behavior of this map here is more complicated. The theories of abelian and metabelian Galois coverings play a substantial role in our analysis and have been used extensively throughout the paper.
