On the connectedness of the branch loci of moduli spaces of orientable Klein surfaces

• Let M K (g,+,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 M K (g,+,k) has a natural orbifold structure with singular locus B K (g,+,k) . If g>2 or k>0 and 2g+k>3 the set B K (g,+,k) consists of the Klein surfaces admitting non-trivial symmetries and we prove that, in this case, the singular locus is connected.

Ämnesord

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

Nyckelord

Klein surface

Riemann surface

Moduli space

Automorphism

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