Costa González, Antonio FélixPorto Ferreira da Silva, Ana María2024-06-142024-06-142019-06-20Costa, 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/s13398-019-00704-61578-7303 | eISSN 1579-1505https://doi.org/10.1007/s13398-019-00704-6https://hdl.handle.net/20.500.14468/22648This 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/s13398-019-00704-6Let 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.eninfo:eu-repo/semantics/openAccess12 Matemáticasjournal articleriemann surfacemoduli spaceorbifoldteichmüller space