AI 中文总结
本文提出一种算法，利用可容许覆盖模空间上三个Hodge丛的比较公式，计算Prym轨迹类的tautological投影，并应用于计算Prym映射次数及证明低亏格下雅可比类的不可整除性。
AI 中文摘要
在阿贝尔簇的模空间中，Prym轨迹参数化与具有固定次数和单值数据的曲线覆盖相关的Prym簇。我们推导并实现了一种计算Prym轨迹类的tautological投影的算法。关键输入是一个比较公式，该公式关联了可容许覆盖模空间上的三个不同的Hodge丛。我们给出了二重和三重覆盖的计算机和手算结果，其中超椭圆雅可比轨迹作为一个特例。随之有两个应用。首先，我们在余维数为零的情形下计算了Prym映射的次数，统一了一系列先前特设的结果。其次，我们在低亏格情形下证明了雅可比类不能被Prym类整除。
英文摘要
In the moduli space of abelian varieties, Prym loci parametrise Prym varieties associated to covers of curves with fixed degree and monodromy data. We derive and implement an algorithm computing the tautological projections of classes of Prym loci. The key input is a comparison formula relating three different Hodge bundles on moduli spaces of admissible covers. We present computer and hand calculations for double and triple covers, with the locus of hyperelliptic Jacobians as a special case. Two applications follow. First, we calculate the degrees of the Prym maps in the codimension-zero cases, unifying a series of previously ad hoc results. Second, we prove in low genera the non-divisibility of the Jacobian class by the Prym class.
Comments92 pages, comments welcome
