Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 51 min ago
PreprintCC BY 4.0arXiv

The inf spectrum of moduli space

  • Ara Basmajian
  • Sayantika Mondal
  • Hugo Parlier
Open at sourcePDFDOICite

Abstract

Given a surface of genus g ≥ 2, its inf spectrum is the ordered multiset of inf lengths of curves on the surface, the infimum being over all hyperbolic metrics. We show that the inf spectrum has exponential growth with coefficients that only depend on g, improving the earlier double exponential upper bound. The proof involves developing a number of tools including the process of "thickening" a surface and the notion of model surfaces. These tools may be of independent interest.

Related

  1. Tremors and horocycle dynamics on the moduli space of transition surfaces
    Jon Chaika, John Smillie, Barak Weiss
    Annals of MathematicsPeer-reviewedLicence not statedFull text22 citedMathematical physicsOpenAlex
  2. The moduli space of curves of genus 16 is uniruled
    Gavril Farkas, Alessandro Verra
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. The Weil-Petersson diameter of moduli space for large genus
    Yunhui Wu
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Hierarchical hyperbolicity, ball quotients, and the moduli space of smooth cubic surfaces
    Daniel Allcock, Alex Wright
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  5. 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

Cite

BibTeXRIS
BibTeX
@misc{basmajian2026spectrum,
  title = {{The inf spectrum of moduli space}},
  author = {Ara Basmajian and Sayantika Mondal and Hugo Parlier},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15926},
  eprint = {2610.15926},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15926},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The inf spectrum of moduli space
AU  - Ara Basmajian
AU  - Sayantika Mondal
AU  - Hugo Parlier
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15926
UR  - https://arxiv.org/abs/2610.15926
AB  - Given a surface of genus g ≥ 2, its inf spectrum is the ordered multiset of inf lengths of curves on the surface, the infimum being over all hyperbolic metrics. We show that the inf spectrum has exponential growth with coefficients that only depend on g, improving the earlier double exponential upper bound. The proof involves developing a number of tools including the process of "thickening" a surface and the notion of model surfaces. These tools may be of independent interest.
ER  -