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One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces

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dc.contributor.authorS. Allen Broughton
dc.contributor.authorCosta González, Antonio Félix
dc.contributor.authorIzquierdo, Milagros
dc.contributor.orcidhttps://orcid.org/0000-0002-9557-9566
dc.date.accessioned2024-06-13T07:46:50Z
dc.date.available2024-06-13T07:46:50Z
dc.date.issued2024
dc.descriptionThe registered version of this article, first published in “Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas", is available online at the publisher's website: Springer, https://orcid.org/0000-0002-9557-9566 La versión registrada de este artículo, publicado por primera vez en “Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas", está disponible en línea en el sitio web del editor: Springer, https://orcid.org/0000-0002-9557-9566
dc.description.abstractThe complex orbifold structure of the moduli space of Riemann surfaces of genus g (g ≥2) produces a stratification into complex subvarieties named equisymmetric strata. Eachequisymmetric stratum is formed by the surfaces where the group ofautomorphisms acts in a topologically equivalent way. The Riemann surfaces in the equisymmetric strata of dimension one are of two structurally different types. Type 1 equisymmetric strata correspond to Riemann surfaces where the group of automorphisms produces a quotient surface of genus zero, while those of Type 2 appear when such a quotient is a surface of genus one. Type 1 equisymmetric strata have been extensively studied by the authors of the present work in a previous recent paper, we now focus on Type 2 strata. We first establish the existence of such strata and their frequency of occurrence in moduli spaces. As a main result we obtain a complete description of Type 2 strata as coverings of the sphere branched over three point (Belyi curves) and where certain isolated points (punctures) have to be eliminated. Finally, we study in detail the doubly infinite family of Type 2 strata whose automorphism groupshave order the product of two primes.en
dc.description.versionversión final
dc.identifier.citationBroughton, S.A., Costa, A.F. & Izquierdo, M. One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 21 (2024). https://doi.org/10.1007/s13398-023-01520-9
dc.identifier.doihttps://doi.org/10.1007/s13398-023-01520-9
dc.identifier.issn1578-7303 | eISSN 1579-1505
dc.identifier.urihttps://hdl.handle.net/20.500.14468/22627
dc.journal.issue21
dc.journal.titleRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
dc.journal.volume118
dc.language.isoen
dc.publisherSpringer
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsriemann surfacees
dc.subject.keywordsmoduli spacees
dc.subject.keywordsautomorphism groupes
dc.subject.keywordsbelyi curvees
dc.titleOne dimensional equisymmetric strata in moduli space with genus 1 quotient surfacesen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery8dbf4941-94eb-4e49-a01e-8b9c32463231
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