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ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4

Published online by Cambridge University Press:  29 March 2010

ANTONIO F. COSTA  and
MILAGROS IZQUIERDO
ANTONIO F. COSTA
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educacin a Distancia, 28040 Madrid, Spain e-mail: acosta@mat.uned.es
MILAGROS IZQUIERDO
Affiliation:
Matematiska Institutionen, Linköpings U 58183 Linköping, Sweden e-mail: miizq@mai.liu.se
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Abstract

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Using uniformization of Riemann surfaces by Fuchsian groups and the equisymmetric stratification of the branch locus of the moduli space of surfaces of genus 4, we prove its connectedness. As a consequence, one can deform a surface of genus 4 with automorphisms, i.e. symmetric, to any other symmetric genus 4 surface through a path consisting entirely of symmetric surfaces.

Keywords

32G1514H15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 401 - 408
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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