Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Len, Yoav, Molcho, Sam, Nabijou, Navid
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213509923