We study the ramified Prym map ${{𝒫}}_{g,r}\to {{𝒜}}_{g-1+\frac{r}{2}}^{\delta }$ which assigns to a ramified double cover of a smooth irreducible curve of genus $g$ ramified in $r$ points the Prym variety of the covering. We focus on the six cases where the dimension of the source is strictly greater than the dimension of the target giving a geometric description of the generic fiber. We also give an explicit example of a totally geodesic curve which is an irreducible component of a fiber of the Prym map ${{𝒫}}_{1,2}$.

中文翻译：

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分枝 Prym 贴图的纤维

我们研究了分叉的 Prym 地图${{𝒫}}_{G,r}\to {{𝒜}}_{G-1+\frac{r}{2}}^{\delta }$它分配给一个平滑的不可约曲线的分枝双覆盖$G$分支于$r$点覆盖的 Prym 品种。我们关注源维度严格大于目标维度的六种情况，给出通用光纤的几何描述。我们还给出了一个完全测地曲线的明确示例，它是 Prym 地图的纤维的不可约组成部分${{𝒫}}_{1,2}$.