Abstract
Let \(\mathcal {M}_{(g,+,k)}^{K}\) be the moduli space of orientable Klein surfaces of genus \(g\) with \(k\) boundary components (see Alling and Greenleaf in Lecture notes in mathematics, vol 219. Springer, Berlin, 1971; Natanzon in Russ Math Surv 45(6):53–108, 1990). The space \(\mathcal {M}_{(g,+,k)} ^{K}\) has a natural orbifold structure with singular locus \(\mathcal {B} _{(g,+,k)}^{K}\). If \(g>2\) or \(k>0\) and \(2g+k>3\) the set \(\mathcal {B} _{(g,+,k)}^{K}\) consists of the Klein surfaces admitting non-trivial symmetries and we prove that, in this case, the singular locus is connected.
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Antonio F. Costa: partially supported by MTM2011-23092.
Milagros Izquierdo: work done during a visit to the Institut Mittag-Leffler (Djursholm, Sweden).
Ana M. Porto: partially supported by MTM2011-23092.
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Costa, A.F., Izquierdo, M. & Porto, A.M. On the connectedness of the branch loci of moduli spaces of orientable Klein surfaces. Geom Dedicata 177, 149–164 (2015). https://doi.org/10.1007/s10711-014-9983-1
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DOI: https://doi.org/10.1007/s10711-014-9983-1