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Counting Cylinders on Z-covers of Genus 2 Square-tiled Surfaces — arXiv:2610.06609

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.06609
License (as archived): CC0-1.0
Archived: 2026-10-06T16:53:44.948Z
SHA-256 of the archived text: ad7a03b639de4a9ca7710c9ee343accbe8740bdddab2c9c9304c6ef7f7f4e0b4
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How to cite

Counting Cylinders on Z-covers of Genus 2 Square-tiled Surfaces — arXiv:2610.06609 — arXiv (en), https://arxiv.org/abs/2610.06609 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5d8df4e8bb59 (Metraipolis archive dc_5d8df4e8bb59, sha256 ad7a03b639de4a9ca7710c9ee343accbe8740bdddab2c9c9304c6ef7f7f4e0b4)

BibTeX

@misc{dc5d8df4e8bb59,
  title = {Counting Cylinders on Z-covers of Genus 2 Square-tiled Surfaces — arXiv:2610.06609},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.06609},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5d8df4e8bb59; sha256 ad7a03b639de4a9ca7710c9ee343accbe8740bdddab2c9c9304c6ef7f7f4e0b4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.06609. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We count maximal cylinders on zero holonomy $\mathbb{Z}$-covers of genus $2$ square-tiled surfaces, up to $\mathbb{Z}$-action, obtaining quadratic asymptotics. We also show that the leading term of the asymptotic, called the Siegel-Veech constant, can be recovered via a large-genus approximation by intermediate finite covers. Our work applies to the infinite staircases introduced by P. Hubert and G. Weitze-Schmithüsen. For many members of this family, we explicitly compute the associated Siegel-Veech constants. In particular, we exhibit the first infinite family of examples of zero holonomy $\mathbb{Z}$-cover in which the number of cylinders grows sub-quadratically.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Dynamical Systems (math.DS) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.06609 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T15:19:20.083Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).