ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 401-408
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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.
COSTA, ANTONIO F.; IZQUIERDO, MILAGROS. ON THE CONNECTEDNESS OF THE BRANCH LOCUS OF THE MODULI SPACE OF RIEMANN SURFACES OF GENUS 4. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 401-408. doi: 10.1017/S0017089510000091
@article{10_1017_S0017089510000091,
author = {COSTA, ANTONIO F. and IZQUIERDO, MILAGROS},
title = {ON {THE} {CONNECTEDNESS} {OF} {THE} {BRANCH} {LOCUS} {OF} {THE} {MODULI} {SPACE} {OF} {RIEMANN} {SURFACES} {OF} {GENUS} 4},
journal = {Glasgow mathematical journal},
pages = {401--408},
year = {2010},
volume = {52},
number = {2},
doi = {10.1017/S0017089510000091},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000091/}
}
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