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PreprintCC BY 4.0arXiv

Genus 4 Supermoduli Space Is Not Projected

  • Ron Donagi
  • Simone Noja
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Abstract

The supermoduli stack Mg, parametrizing smooth unpunctured super Riemann surfaces of genus g, is known to be non-projected for g ≥ 5. We extend this result to the even-spin component of M4. This is done by exhibiting an appropriate compact curve in the spin moduli space 𝒮ℳ4+, and computing the restriction to it of the class obstructing the projectedness of M4+. This restriction turns out to be non-zero, proving that M4+ is non-projected.

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Cite

BibTeXRIS
BibTeX
@misc{donagi2026genus,
  title = {{Genus 4 Supermoduli Space Is Not Projected}},
  author = {Ron Donagi and Simone Noja},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.24996},
  eprint = {2608.24996},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.24996},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Genus 4 Supermoduli Space Is Not Projected
AU  - Ron Donagi
AU  - Simone Noja
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.24996
UR  - https://arxiv.org/abs/2608.24996
AB  - The supermoduli stack M_g, parametrizing smooth unpunctured super Riemann surfaces of genus g, is known to be non-projected for g ≥ 5. We extend this result to the even-spin component of M_4. This is done by exhibiting an appropriate compact curve in the spin moduli space 𝒮ℳ_4^+, and computing the restriction to it of the class obstructing the projectedness of M_4^+. This restriction turns out to be non-zero, proving that M_4^+ is non-projected.
ER  -