Helmut Völklein

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Let G be a finite group, and g ≥ 2. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves with prescribed automorphism group G. We completely classify these loci for g = 3 (including equations for the corresponding curves), and for g ≤ 10 we classify those(More)
where Πg(C) is the geometric (profinite) fundamental group of C×Spec(Ks) (i.e. Πg(C) is equal to the Galois group of the maximal unramified extension of F (C)⊗Ks). This sequence induces a homomorphism ρC from GK to Out(Πg(C)) which is the group of automorphisms modulo inner automorphisms of Πg(C). It is well known that ρC is an important tool for studying(More)
Let G be a finite group. By Riemann’s Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic curves require the computation of braid orbits. In this paper we describe an implementation of this computation. We discuss(More)
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