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PreprintCC BY-NC-ND 4.0arXiv

Hierarchical hyperbolicity, ball quotients, and the moduli space of smooth cubic surfaces

  • Daniel Allcock
  • Alex Wright
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Abstract

We prove that the orbifold fundamental group of the moduli space of smooth complex cubic surfaces is a hierarchically hyperbolic group. This places it within a powerful geometric framework whose prototypical examples are mapping class groups. The proof uses a known incomplete complex hyperbolic metric on the moduli space, and applies in a broader setting which includes a number of other moduli spaces.

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Cite

BibTeXRIS
BibTeX
@misc{allcock2026hierarchical,
  title = {{Hierarchical hyperbolicity, ball quotients, and the moduli space of smooth cubic surfaces}},
  author = {Daniel Allcock and Alex Wright},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14416},
  eprint = {2609.14416},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14416},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Hierarchical hyperbolicity, ball quotients, and the moduli space of smooth cubic surfaces
AU  - Daniel Allcock
AU  - Alex Wright
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14416
UR  - https://arxiv.org/abs/2609.14416
AB  - We prove that the orbifold fundamental group of the moduli space of smooth complex cubic surfaces is a hierarchically hyperbolic group. This places it within a powerful geometric framework whose prototypical examples are mapping class groups. The proof uses a known incomplete complex hyperbolic metric on the moduli space, and applies in a broader setting which includes a number of other moduli spaces.
ER  -