One-dimensional families of Riemann surfaces of genus g with 4g+4automorphims
نویسندگان
چکیده
We prove that the maximal number ag + b of automorphisms of equisymmetric and complex-uniparametric families of Riemann surfaces appearing in all genera is 4g+ 4. For each integer g ≥ 2 we find an equisymmetric complex-uniparametric family Ag of Riemann surfaces of genus g having automorphism group of order 4g + 4. For g ≡ −1mod4 we present another uniparametric family Kg with automorphism group of order 4g + 4. The family Ag contains the Accola-Maclachlan surface and the family Kg contains the Kulkarni surface. Mathematics Subject Classification (2000) MSC 30F10 · MSC 14H15 · 14F37
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