分叉的Prym图的纤维

arXiv: Algebraic Geometry Pub Date : 2020-07-04 DOI:10.1142/S0219199721500309

P. Frediani, J. Naranjo, I. Spelta

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引用次数: 5

摘要

我们研究了分枝Prym图$\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}$，它分配给一个分枝双重覆盖的光滑不可约曲线属$g$，分枝在$r$点覆盖的Prym变化。我们专注于六种情况，其中源的尺寸严格大于给出通用纤维的几何描述的目标的尺寸。我们还给出了一个完全测地线曲线的显式例子，它是Prym图${\mathcal P}_{1,2}$的纤维的不可约分量。

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The fibers of the ramified Prym map

We study the ramified Prym map $\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}$ 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 fibre. We also give an explicit example of a totally geodesic curve which is an irreducible component of a fibre of the Prym map ${\mathcal P}_{1,2}$.

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arXiv: Algebraic Geometry

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