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The fibers of the ramified Prym map
Communications in Contemporary Mathematics ( IF 1.2 ) Pub Date : 2021-05-21 , DOI: 10.1142/s0219199721500309
Paola Frediani 1 , Juan Carlos Naranjo 2 , Irene Spelta 1
Affiliation  

We study the ramified Prym map 𝒫g,r𝒜g1+r2δ 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 𝒫1,2.



中文翻译:

分枝 Prym 贴图的纤维

我们研究了分叉的 Prym 地图𝒫G,r𝒜G-1+r2δ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𝒫1,2.

更新日期:2021-05-21
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