There are no primitive Teichmüller curves in $\mathrm{Prym}(2,2)$

Julien Boulanger; Sam Freedman

doi:10.5802/crmath.551

Research article - Geometry and Topology

There are no primitive Teichmüller curves in

Prym (2, 2)

Julien Boulanger ¹; Sam Freedman ²

¹ France
² United States

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 167-170.

Abstract
Résumé

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

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

Received: 2023-01-31
Accepted: 2023-07-25
Published online: 2024-03-07

DOI: 10.5802/crmath.551

Author's affiliations:

Julien Boulanger ¹; Sam Freedman ²

¹ France
² United States

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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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/

References
Cited by

[1] Matt Bainbridge; Philipp Habegger; Martin Möller Teichmüller curves in genus three and just likely intersections in $G_{m}^{n} \times G_{a}^{n}$ , 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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