Teichmueller curves generated by Weierstrass Prym eigenforms in genus three and genus four
| hal.structure.identifier | Institut Fourier [IF ] | |
| dc.contributor.author | LANNEAU, Erwan | |
| hal.structure.identifier | Équipe Géométrie | |
| dc.contributor.author | NGUYEN, Duc-Manh | |
| dc.date.accessioned | 2024-04-04T02:18:19Z | |
| dc.date.available | 2024-04-04T02:18:19Z | |
| dc.date.created | 2011-11-09 | |
| dc.date.issued | 2014-06-02 | |
| dc.identifier.issn | 1753-8424 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189301 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique - ANR-11-LABX-0025 | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press | |
| dc.subject | surface de translation | |
| dc.subject | courbe de Teichmuller | |
| dc.title.en | Teichmueller curves generated by Weierstrass Prym eigenforms in genus three and genus four | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1112/jtopol/jtt036 | |
| dc.subject.hal | Mathématiques [math]/Topologie géométrique [math.GT] | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.identifier.arxiv | 1111.2299 | |
| bordeaux.journal | Journal of topology | |
| bordeaux.page | 475-522 | |
| bordeaux.volume | 7 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00988379 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00988379v1 | |
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