LANNEAU, Erwan; NGUYEN, Duc-Manh

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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

Annales Scientifiques de l'École Normale Supérieure. 2016, vol. 49, n° 1, p. 87-30

Société mathématique de France

Résumé en anglais

This paper deals with Prym eigenforms which are introduced previously by McMullen. We prove several results on the directional flow on those surfaces, related to complete periodicity (introduced by Calta). More precisely we show that any homological direction is algebraically periodic, and any direction of a regular closed geodesic is a completely periodic direction. As a consequence we draw that the limit set of the Veech group of every Prym eigenform in some Prym loci of genus 3,4, and 5 is either empty, one point, or the full circle at infinity. We also construct new examples of translation surfaces satisfying the topological Veech dichotomy. As a corollary we obtain new translation surfaces whose Veech group is infinitely generated and of the first kind.< Réduire

Mots clés en anglais

Prym eigenform

moduli space

translation surface

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194176

Project ANR

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

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251