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PreprintCC BY 4.0arXiv

Special Loci in the Moduli of Curves

  • David Urbanik
  • Ziquan Yang
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Abstract

We introduce new techniques to study mixed-characteristic special loci in moduli spaces and give several applications, focusing in particular on the moduli space Mg of curves. These applications include Zariski density results for split Jacobians, non-density results for supersingular loci, and lifting results for algebraic cycles, all under appropriate numerical conditions. Our methods generalize to more-or-less arbitrary moduli spaces mapping to Hodge-type Shimura varieties (and even some settings beyond the Shimura case), and relate to questions raised by Oort and de Jong.

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Cite

BibTeXRIS
BibTeX
@misc{urbanik2026special,
  title = {{Special Loci in the Moduli of Curves}},
  author = {David Urbanik and Ziquan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08382},
  eprint = {2610.08382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08382},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Special Loci in the Moduli of Curves
AU  - David Urbanik
AU  - Ziquan Yang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08382
UR  - https://arxiv.org/abs/2610.08382
AB  - We introduce new techniques to study mixed-characteristic special loci in moduli spaces and give several applications, focusing in particular on the moduli space M_g of curves. These applications include Zariski density results for split Jacobians, non-density results for supersingular loci, and lifting results for algebraic cycles, all under appropriate numerical conditions. Our methods generalize to more-or-less arbitrary moduli spaces mapping to Hodge-type Shimura varieties (and even some settings beyond the Shimura case), and relate to questions raised by Oort and de Jong.
ER  -