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

Autor:	Antonio F. Costa, Milagros Izquierdo, Ana M. Porto
Rok vydání:	2014
Předmět:	Riemann surface Hyperbolic geometry Geometry Klein surface Algebraic geometry Automorphism Moduli space Combinatorics symbols.namesake Genus (mathematics) Homogeneous space symbols Geometri Geometry and Topology Orbifold Mathematics
Zdroj:	Geometriae Dedicata. 177:149-164
ISSN:	1572-9168 0046-5755
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::202960fb95ba0b0fc0818c8f9362e798 https://doi.org/10.1007/s10711-014-9983-1 Zobrazit plný text záznamu Full text from SpringerLink