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hal.structure.identifierInstitut Fourier [IF ]
dc.contributor.authorLANNEAU, Erwan
hal.structure.identifierÉquipe Géométrie
dc.contributor.authorNGUYEN, Duc-Manh
dc.date.accessioned2024-04-04T02:18:19Z
dc.date.available2024-04-04T02:18:19Z
dc.date.created2011-11-09
dc.date.issued2014-06-02
dc.identifier.issn1753-8424
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189301
dc.description.abstractEnThis 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.sponsorshipSystemes et Algorithmes Pervasifs au confluent des mondes physique et numérique - ANR-11-LABX-0025
dc.language.isoen
dc.publisherOxford University Press
dc.subjectsurface de translation
dc.subjectcourbe de Teichmuller
dc.title.enTeichmueller curves generated by Weierstrass Prym eigenforms in genus three and genus four
dc.typeArticle de revue
dc.identifier.doi10.1112/jtopol/jtt036
dc.subject.halMathématiques [math]/Topologie géométrique [math.GT]
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
dc.identifier.arxiv1111.2299
bordeaux.journalJournal of topology
bordeaux.page475-522
bordeaux.volume7
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00988379
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00988379v1
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