Details

Autor(en) / Beteiligte

• Bujalance, José A.
• Costa, Antonio F.
• Porto, Ana M.

Titel

On the topological types of symmetries of elliptic-hyperelliptic Riemann surfaces

Ist Teil von

• Israel journal of mathematics, 2004-01, Vol.140 (1), p.145-155

Ort / Verlag

Heidelberg: Springer Nature B.V

Erscheinungsjahr

2004

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• LetX be a Riemann surface of genusg. The surfaceX is called elliptic-hyperelliptic if it admits a conformal involutionh such that the orbit spaceX/〈h〉 has genus one. The involutionh is then called an elliptic-hyperelliptic involution. Ifg>5 then the involutionh is unique, see [A]. We call symmetry to any anticonformal involution ofX. LetAut±(X) be the group of conformal and anticonformal automorphisms ofX and letσ, τ be two symmetries ofX with fixed points and such that {σ, hσ} and {τ, hτ} are not conjugate inAut±(X). We describe all the possible topological conjugacy classes of {σ, σh, τ, τh}. As consequence of our study we obtain that, in the moduli space of complex algebraic curves of genusg (g even >5), the subspace whose elements are the elliptic-hyperelliptic real algebraic curves is not connected. This fact contrasts with the result in [Se]: the subspace whose elements are the hyperelliptic real algebraic curves is connected.