LANNEAU, Erwan; NGUYEN, Duc-Manh

doi:10.1112/jtopol/jtt036

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LANNEAU, Erwan
Institut Fourier [IF ]

NGUYEN, Duc-Manh
Équipe Géométrie

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Article de revue

Ce document a été publié dans

Journal of topology. 2014-06-02, vol. 7, n° 2, p. 475-522

Oxford University Press

Résumé en anglais

This paper is devoted to the classification of the infinite families of Teichmuller curves generated by Prym eigenforms of genus 3 having a single zero. These curves were discovered by McMullen. The main invariants of our classification is the discriminant D of the corresponding quadratic order, and the generators of this order. It turns out that for D sufficiently large, there are two Teichmueller curves when D=1 modulo 8, only one Teichmueller curve when D=0,4 modulo 8, and no Teichmueller curves when D=5 modulo 8. For small values of D, where this classification is not necessarily true, the number of Teichmueller curves can be determined directly. The ingredients of our proof are first, a description of these curves in terms of prototypes and models, and then a careful analysis of the combinatorial connectedness in the spirit of McMullen. As a consequence, we obtain a description of cusps of Teichmueller curves given by Prym eigenforms. We would like also to emphasis that even though we have the same statement compared to, when D=1 modulo 8, the reason for this disconnectedness is different. The classification of these Teichmueller curves plays a key role in our investigation of the dynamics of SL(2,R) on the intersection of the Prym eigenform locus with the stratum H(2,2), which is the object of a forthcoming paper.< Réduire

Mots clés

surface de translation

courbe de Teichmuller

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189301

DOI

http://dx.doi.org/10.1112/jtopol/jtt036

Project ANR

Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique - ANR-11-LABX-0025

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251