no. 3
The Galois Action and a Spin Invariant for Prym-Teichmüller Curves in Genus 3
[L’action galoisienne et un invariant spin pour les courbes de Prym-Teichmüller en genre 3]
Zachhuber, Jonathan1
1FB 12 – Institut für Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Str. 6–8, D-60325 Frankfurt am Main
Bulletin de la Société Mathématique de France, Tome 146 (2018) no. 3, pp. 427-439

Given a Prym-Teichmüller curve in ℳ3, this note provides an invariant that sorts the cusp prototypes of Lanneau and Nguyen by component. This can be seen as an analog of McMullen’s genus 2 spin invariant, although the source of this invariant is different. Moreover, we describe the Galois action on the cusps of these Teichmüller curves, extending the results of Bouw and Möller in genus 2. We use this to show that the components of the genus 3 Prym-Teichmüller curves are homeomorphic.

Étant donnée une courbe de Prym–Teichmüller dans ℳ3, cette note introduit un invariant qui trie par composante les prototypes cusp de Lanneau et Nguyen. Il peut être vu comme l’analogue en genre 3 de l’invariant spin en genre 2 de McMullen, bien que la source de cet invariant soit différente. De plus, nous décrivons l’action de Galois sur les cusps des courbes de Teichmüller, étendant les résultats en genre 2 de Bouw et Möller. Cela nous permet de montrer que les composants des courbes de Prym–Teichmüller en genre 3 sont homéomorphes.

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DOI : 10.24033/bsmf.2766
Classification : 14H10, 32G15, 57R18, 54F65, 37D50
Keywords: Teichmüller curves, cusps, spin invariant.
Mots-clés : Courbes de Teichmüller, cusps, invariant spin.

Zachhuber, Jonathan  1

1 FB 12 – Institut für Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Str. 6–8, D-60325 Frankfurt am Main 
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     title = {The {Galois} {Action} and a {Spin} {Invariant} for {Prym-Teichm\"uller} {Curves} in {Genus} 3},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
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Zachhuber, Jonathan. The Galois Action and a Spin Invariant for Prym-Teichmüller Curves in Genus 3. Bulletin de la Société Mathématique de France, Tome 146 (2018) no. 3, pp. 427-439. doi: 10.24033/bsmf.2766

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