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Hodge integrals on admissible covers and tautological projections of Prym classes

  • Yoav Len
  • Sam Molcho
  • Navid Nabijou
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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.

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Cite

BibTeXRIS
BibTeX
@misc{len2026hodge,
  title = {{Hodge integrals on admissible covers and tautological projections of Prym classes}},
  author = {Yoav Len and Sam Molcho and Navid Nabijou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17703},
  eprint = {2609.17703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17703},
}
RIS
TY  - UNPB
TI  - Hodge integrals on admissible covers and tautological projections of Prym classes
AU  - Yoav Len
AU  - Sam Molcho
AU  - Navid Nabijou
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17703
UR  - https://arxiv.org/abs/2609.17703
AB  - 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.
ER  -