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Algebraic intersection for translation surfaces in the stratum (2)
[Intersection algébrique dans la strate (2) des surfaces de translation]
Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 65-70.

Nous étudions une quantité KVol liée au volume sur la strate (2) des surfaces de translation de genre 2, avec une singularité conique. Nous donnons une suite explicite de surfaces L(n,n) telles que KVol(L(n,n))2 quand n tend vers l’infini, 2 étant l’infimum conjectural de KVol sur (2).

We study a volume related quantity KVol on the stratum (2) of translation surfaces of genus 2, with one conical point. We provide an explicit sequence L(n,n) of surfaces such that KVol(L(n,n))2 when n goes to infinity, 2 being the conjectured infimum for KVol over (2).

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.153

Smail Cheboui 1, 2 ; Arezki Kessi 2 ; Daniel Massart 1

1 IMAG, Univ Montpellier, CNRS, Montpellier, France
2 USTHB, Faculté de Mathématiques, Laboratoire de Systèmes Dynamiques, 16111 El-Alia BabEzzouar, Alger, Algérie
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {Smail Cheboui and Arezki Kessi and Daniel Massart},
     title = {Algebraic intersection for translation surfaces in the stratum ${\protect \mathcal{H}(2)}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {65--70},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
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     year = {2021},
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     language = {en},
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Smail Cheboui; Arezki Kessi; Daniel Massart. Algebraic intersection for translation surfaces in the stratum ${\protect \mathcal{H}(2)}$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 65-70. doi : 10.5802/crmath.153. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.153/

[1] Smaïl Cheboui; Arezki Kessi; Daniel Massart Algebraic intersection for translation surfaces in the Teichmüller disk of L(2,2) (https://arxiv.org/abs/2007.10847)

[2] Frank Herrlich; Bjoern Muetzel; Gabriela Weitze-Schmithüsen Systolic geometry of translation surfaces (2018) (https://arxiv.org/abs/1809.10327v1)

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[7] Gabriela Schmithüsen An algorithm for finding the Veech group of an origami, Exp. Math., Volume 13 (2004) no. 4, pp. 459-472 | DOI | MR | Zbl

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