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On the connectedness of the branch locus of moduli space of hyperelliptic Klein surfaces with one boundary

Antonio F. Costa

http://orcid.org/0000-0002-9905-0264

Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, 28040 Madrid, Spain

E-mail Address: acosta@mat.uned.es

Corresponding author.

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Milagros Izquierdo

Matematiska Institutionen, Linköpings Universitet, 581 83 Linköping, Sweden

E-mail Address: milagros.izquierdo@liu.se

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, and

Ana Maria Porto

Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, 28040 Madrid, Spain

E-mail Address: asilva@mat.uned.es

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https://doi.org/10.1142/S0129167X17500380Cited by:2 (Source: Crossref)

Abstract

In this work, we prove that the hyperelliptic branch locus of orientable Klein surfaces of genus $g$ with one boundary component is connected and in the case of non-orientable Klein surfaces it has $\frac{g + 1}{2}$ components, if $g$ is odd, and $\frac{g + 2}{2}$ components for even $g$ . We notice that, for non-orientable Klein surfaces with two boundary components, the hyperelliptic branch loci are connected for all genera.

To the memory of Mika Seppälä

Keywords:

AMSC: 30F10, 30F50, 14H15, 20H10

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