Skip to content
DraconiticResearch
Search Sources API
178,033 studies31 sourcesUpdated 44 min ago
PreprintCC BY 4.0arXiv

Supermoduli spaces are non-projected in every genus g≥ 3

  • Mauricio Corrêa
  • Ron Donagi
  • Simone Noja
Open at sourcePDFDOICite

Abstract

We prove that, for every genus g≥ 3, the primary obstruction of each parity component of the moduli superstack of smooth unpunctured super Riemann surfaces is nonzero, both algebraically and holomorphically. Consequently, both components are non-projected and, in particular, non-split: neither admits an algebraic or holomorphic retraction onto its reduced moduli stack of spin curves.

Related

  1. Genus 4 Supermoduli Space Is Not Projected
    Ron Donagi, Simone Noja
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsarXiv
  2. Every Closed Oriented Surface of Positive Genus Is Loewner
    Qiongling Li
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. The Last Iterate of the Projected Stochastic Subgradient Method Pays a Logarithm, Even in Dimension One
    Guglielmo Beretta, Tommaso Cesari, Roberto Colomboni
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  4. Initialization Stability and Convergence of Projected Langevin Dynamics
    Qi Feng, Nathan Sauldubois, Xin Zhang
    arXivPreprintCC BY 4.0Full textOptimisation & controlProbabilityarXiv
  5. Estimating Average Treatment Effects with Projected Instrumental Variables
    Shuyuan Chen, Yifan Cui
    arXivPreprintarXiv licenceFull textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{correa2026supermoduli,
  title = {{Supermoduli spaces are non-projected in every genus $g\geq 3$}},
  author = {Mauricio Corrêa and Ron Donagi and Simone Noja},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00490},
  eprint = {2610.00490},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00490},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Supermoduli spaces are non-projected in every genus g≥ 3
AU  - Mauricio Corrêa
AU  - Ron Donagi
AU  - Simone Noja
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00490
UR  - https://arxiv.org/abs/2610.00490
AB  - We prove that, for every genus g≥ 3, the primary obstruction of each parity component of the moduli superstack of smooth unpunctured super Riemann surfaces is nonzero, both algebraically and holomorphically. Consequently, both components are non-projected and, in particular, non-split: neither admits an algebraic or holomorphic retraction onto its reduced moduli stack of spin curves.
ER  -