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There are no primitive Teichmüller curves in Prym(2,2)
[Il n’y a pas de courbes de Teichmüller primitives dans Prym(2,2)]
Julien Boulanger1 ; Sam Freedman2 
1 France
2 United States
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 167-170.

Nous terminons un travail initié par Lanneau et Möller [4] en montrant qu’il n’existe pas de courbes de Teichmüller primitives dans Prym(2,2).

We complete the work of Lanneau–Möller [4] to show that there are no primitive Teichmüller curves in Prym(2,2).

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.551
Julien Boulanger 1 ; Sam Freedman 2

1 France
2 United States
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Julien Boulanger and Sam Freedman},
     title = {There are no primitive {Teichm\"uller} curves in $\mathrm{Prym}(2,2)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {167--170},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.551},
     language = {en},
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Julien Boulanger; Sam Freedman. There are no primitive Teichmüller curves in $\mathrm{Prym}(2,2)$. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 167-170. doi : 10.5802/crmath.551. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.551/

[1] Matt Bainbridge; Philipp Habegger; Martin Möller Teichmüller curves in genus three and just likely intersections in G m n ×G a n , Publ. Math., Inst. Hautes Étud. Sci., Volume 124 (2014), pp. 1-98 | DOI | Zbl

[2] Vincent Delecroix; Julian Rüth A new orbit closure in genus 8? (2021) | arXiv | DOI

[3] Pascal Hubert; Thomas Schmidt An Introduction to Veech Surfaces, Handbook of dynamical systems. Volume 1B, Elsevier, 2006, pp. 501-526 | Zbl

[4] Erwan Lanneau; Martin Moeller Non-Existence and Finiteness Results for Teichmüller Curves in Prym Loci, Exp. Math., Volume 31 (2019), pp. 621-636 | DOI | Zbl

[5] Curtis T. McMullen Teichmüller curves in genus two: Torsion divisors and ratios of sines, Invent. Math., Volume 165 (2006) no. 3, pp. 651-672 | DOI | Zbl

[6] Curtis T. McMullen Dynamics of SL 2 (ℝ) over moduli space in genus two, Ann. Math., Volume 165 (2007) no. 2, pp. 397-456 | DOI | MR | Zbl

[7] Curtis T. McMullen Billiards and Teichmülller curves (2021) (https://people.math.harvard.edu/~ctm/papers/home/text/papers/tsurv/tsurv.pdf)

[8] Martin Möller Geometry of Teichmüller curves, Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. III. Invited lectures, World Scientific (2018), pp. 2017-2034 | DOI | Zbl

[9] Karl Winsor Uniqueness of the Veech 14-gon (2022) | arXiv | DOI

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