Publicación: Note on topologically singular points in themoduli space of Riemann surfaces of genus 2
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2019-06-20
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Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Springer
Resumen
Let Mg be the moduli space of Riemann surfaces of genus g. Rauch (Bull Am Math Soc 68:390–394, 1962) focused his attention on and determined the so-called topological singular points ofMg: these are the points ofMg whose neighbourhoods are not homeomorphic to a ball. In a previous paper, the authors produced a topological proof for Rauch’s result for genera > 2; however, the methods used there do not apply to the genus 2 case. The only known proof for the remaining and important case, i.e., the case of singular points inM2, is to be found in an article by Igusa (Ann Math 72(3):612–649, 1960) and it lays on methods from algebraic geometry. Here, we present a topological proof for this case too.
Descripción
This is the Accepted Manuscript of an article published by Springer in " Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas" on Jun 2019, available online: https://doi.org/10.1007/s13398-019-00704-6
Este es el manuscrito aceptado de un artículo publicado por Springer en "Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas" en Jun 2019, disponible en línea: https://doi.org/10.1007/s13398-019-00704-6
Categorías UNESCO
Palabras clave
riemann surface, moduli space, orbifold, teichmüller space
Citación
Costa, A.F., Porto, A.M. Note on topologically singular points in the moduli space of Riemann surfaces of genus 2. RACSAM 113, 3375–3382 (2019). https://doi.org/10.1007/s13398-019-00704-6
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Facultad de Ciencias
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Matemáticas Fundamentales