Complete periodicity of Prym eigenforms
Language
en
Article de revue
This item was published in
Annales Scientifiques de l'École Normale Supérieure. 2016, vol. 49, n° 1, p. 87-30
Société mathématique de France
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Prym eigenform
moduli space
translation surface
ANR Project
Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique - ANR-11-LABX-0025
Origin
Hal imported