论文标题
至少6分的全球Prym-torelli，双重覆盖
Global Prym-Torelli for double coverings ramified in at least 6 points
论文作者
论文摘要
We prove that the ramified Prym map $\mathcal P_{g, r}$ which sends a covering $π:D\longrightarrow C$ ramified in $r$ points to the Prym variety $P(π):=\text{Ker}(\text{Nm}_π)$ is an embedding for all $r\ge 6$ and for all $g(C)>0$.此外，通过研究限制到过椭圆曲线的覆盖物源，我们表明$ \ MATHCAL P_ {G，2} $和$ \ MATHCAL P_ {G，4} $具有阳性尺寸纤维。
We prove that the ramified Prym map $\mathcal P_{g, r}$ which sends a covering $π:D\longrightarrow C$ ramified in $r$ points to the Prym variety $P(π):=\text{Ker}(\text{Nm}_π)$ is an embedding for all $r\ge 6$ and for all $g(C)>0$. Moreover, by studying the restriction to the locus of coverings of hyperelliptic curves, we show that $\mathcal P_{g, 2}$ and $\mathcal P_{g, 4}$ have positive dimensional fibers.
