no. 1
Géométrie différentielle
Algebraic intersection for translation surfaces in the stratum ℋ(2)
[Intersection algébrique dans la strate ℋ(2) des surfaces de translation]
Cheboui, Smail1, 2 ; Kessi, Arezki1 ; Massart, Daniel2 
1 USTHB, Faculté de Mathématiques, Laboratoire de Systèmes Dynamiques, 16111 El-Alia BabEzzouar, Alger, Algérie
2 IMAG, Univ Montpellier, CNRS, Montpellier, France
Comptes Rendus. Mathématique, Tome 359 (2021) no. 1, pp. 65-70

We study a volume related quantity KVol on the stratum ℋ(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 ℋ(2).

Nous étudions une quantité KVol liée au volume sur la strate ℋ(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 ℋ(2).

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

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

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

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

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