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$\mathrm{GL}^+(2,\mathbb{R})$-orbits in Prym eigenform loci

hal.structure.identifierInstitut Fourier [IF ]
dc.contributor.authorLANNEAU, Erwan
hal.structure.identifierÉquipe Géométrie
dc.contributor.authorNGUYEN, Duc-Manh
dc.date.accessioned2024-04-04T03:16:00Z
dc.date.available2024-04-04T03:16:00Z
dc.date.issued2016-07-04
dc.identifier.issn1465-3060
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194177
dc.description.abstractEnThis paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials. We show that the following dichotomy holds: an orbit is either closed or dense in a connected component of the Prym eigenform locus. The proof uses several topological properties of Prym eigenforms, which are proved by the authors in a previous work. In particular the tools and the proof are independent of the recent results of Eskin-Mirzakhani-Mohammadi. As an application we obtain a finiteness result for the number of closed GL^+(2,R)-orbits (not necessarily primitive) in the Prym eigenform locus Prym_D(2,2) for any fixed D that is not a square.
dc.description.sponsorshipSystemes et Algorithmes Pervasifs au confluent des mondes physique et numérique - ANR-11-LABX-0025
dc.language.isoen
dc.publisherMathematical Sciences Publishers
dc.subject.enmoduli space
dc.subject.enPrym eigenform
dc.subject.entranslation surface
dc.title.en$\mathrm{GL}^+(2,\mathbb{R})$-orbits in Prym eigenform loci
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Topologie géométrique [math.GT]
dc.identifier.arxiv1310.8537
bordeaux.journalGeometry and Topology
bordeaux.page1359-1426
bordeaux.volume20
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01258856
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01258856v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Geometry%20and%20Topology&rft.date=2016-07-04&rft.volume=20&rft.issue=3&rft.spage=1359-1426&rft.epage=1359-1426&rft.eissn=1465-3060&rft.issn=1465-3060&rft.au=LANNEAU,%20Erwan&NGUYEN,%20Duc-Manh&rft.genre=article


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