Skip to content
DraconiticResearch
Search Sources API
181,686 studies31 sourcesUpdated 16 min ago
PreprintCC BY 4.0arXiv

The Weil-Petersson diameter of moduli space for large genus

  • Yunhui Wu
Open at sourcePDFDOICite

Abstract

We determine the large-genus order of the Weil-Petersson diameter of ℳg,n for each fixed number of punctures: namely, diam(ℳg,n)asymp√glog g. The main new ingredient is an integrated Ricci estimate for geodesics that minimize in moduli space and have thick endpoints, with no systole bound along their interiors.

Related

  1. No Shortcuts to Infinity: Weil-Petersson Distance in Calabi-Yau Complex Structure Moduli Space
    Jeroen Monnee
    arXivPreprintarXiv licenceFull textAlgebra & number theoryHigh-energy & particle physicsarXiv
  2. The moduli space of curves of genus 16 is uniruled
    Gavril Farkas, Alessandro Verra
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. A complete curve of genus 5 in the moduli space of curves of genus 3 and related questions
    Samuel Grushevsky, Christophe Ritzenthaler
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Uniform large-genus asymptotics of Weil-Petersson volumes
    Zhiyi Li, Qihang Wang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryGeometry & topologyarXiv
  5. The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings
    Luca Battistella, Andrea Di Lorenzo, Michele Pernice
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{wu2026weilpetersson,
  title = {{The Weil-Petersson diameter of moduli space for large genus}},
  author = {Yunhui Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19707},
  eprint = {2610.19707},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19707},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Weil-Petersson diameter of moduli space for large genus
AU  - Yunhui Wu
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19707
UR  - https://arxiv.org/abs/2610.19707
AB  - We determine the large-genus order of the Weil-Petersson diameter of ℳ_g,n for each fixed number of punctures: namely, diam(ℳ_g,n)asymp√glog g. The main new ingredient is an integrated Ricci estimate for geodesics that minimize in moduli space and have thick endpoints, with no systole bound along their interiors.
ER  -