Publication: One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces
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Date
2024
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info:eu-repo/semantics/openAccess
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Springer
Abstract
The 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.
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The 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
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Keywords
riemann surface, moduli space, automorphism group, belyi curve
Citation
Broughton, 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
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Facultad de Ciencias
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Matemáticas Fundamentales