Abstract:In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p ≥ 3 is a prime integer and the genus of the surfaces is at least (p − 1) 2 + 1. We use Fuchsian and NEC groups, and cohomology of finite groups.
“…The previous result allows us to find a list of automorphism groups of trigonal curves (see also [2]). This list is obtained by an easy combination of [31, Table 7], [5, Table 1] and [18], plus the computation of the reduced groups which are not in the original tables.…”
Section: Known Facts About 3−gonal Curves and Their Automorphismsmentioning
confidence: 96%
“…(3) we obtain that the Jacobian variety J X associated to X is completely decomposable i.e. Table 4 Decomposition of the induced representation by the trivial one on each class of conjugation of subgroups of G L (2,3) Classes of subgroups Identity element 1 1 2 2 2 3 3 4 O r d e r2 ,l e n g t h1 In this case, choosing H 1 and H 2 as before ν × : B 41 × B 42 → J X is an isomorphism. Hence |Ker(ν)| = 1.…”
Section: Theoremmentioning
confidence: 99%
“…To give an explicit description of the subgroups of G L (2,3) giving the smallest order for the kernel of ν × , we consider the above presentation of G L(2, 3) and the same generating vector (a, b, ab). Set H = ab , and consider the following subgroups of order 2 in G L(2, 3)…”
Artículo de publicación ISIGiven a compact Riemann surface X with an action of a finite group G, the group algebra provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely build a decomposition of this kind. Our method allows us to study the geometry of the decomposition. For instance, we build several decompositions in order to determine which one has kernel of smallest order. We apply this method to families of trigonal curves up to genus 10.Fondecyt 110011
“…The previous result allows us to find a list of automorphism groups of trigonal curves (see also [2]). This list is obtained by an easy combination of [31, Table 7], [5, Table 1] and [18], plus the computation of the reduced groups which are not in the original tables.…”
Section: Known Facts About 3−gonal Curves and Their Automorphismsmentioning
confidence: 96%
“…(3) we obtain that the Jacobian variety J X associated to X is completely decomposable i.e. Table 4 Decomposition of the induced representation by the trivial one on each class of conjugation of subgroups of G L (2,3) Classes of subgroups Identity element 1 1 2 2 2 3 3 4 O r d e r2 ,l e n g t h1 In this case, choosing H 1 and H 2 as before ν × : B 41 × B 42 → J X is an isomorphism. Hence |Ker(ν)| = 1.…”
Section: Theoremmentioning
confidence: 99%
“…To give an explicit description of the subgroups of G L (2,3) giving the smallest order for the kernel of ν × , we consider the above presentation of G L(2, 3) and the same generating vector (a, b, ab). Set H = ab , and consider the following subgroups of order 2 in G L(2, 3)…”
Artículo de publicación ISIGiven a compact Riemann surface X with an action of a finite group G, the group algebra provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely build a decomposition of this kind. Our method allows us to study the geometry of the decomposition. For instance, we build several decompositions in order to determine which one has kernel of smallest order. We apply this method to families of trigonal curves up to genus 10.Fondecyt 110011
“…By the Remark 1 if (a, b) is maximal (a, b) ≥ (4, 0), then by [8], [10], [12] the signature s (a,b) must be of the form either (0; [2, 2, 2, n]), n ≥ 3 or (0; [2,2,3, n]) with 3 ≤ n ≤ 5.…”
“…The p-gonal surfaces are cyclic p-fold coverings of the Riemann sphere and there is a great deal of interest in the study of the automorphism groups of these surfaces (see for instance [4,2,3,15,20]). The groups of (conformal and anticonformal) automorphisms of p-gonal real Riemann surfaces are obtained in [2], under the assumption that the group generated by a p-gonal morphism is normal; for the conformal automorphisms in the non-normal case see [20].…”
Abstract. In this article we prove that the full automorphism group of a cyclic p-gonal pseudo-real Riemann surface of genus g is either a semidirect product C n ⋉ C p or a cyclic group, where p is a prime > 2 and g > (p − 1) 2 . We obtain necessary and sufficient conditions for the existence of a cyclic p-gonal pseudo-real Riemann surface with full automorphism group isomorphic to a given finite group. Finally we describe some families of cyclic p-gonal pseudo-real Riemann surfaces where the order of the full automorphism group is maximal and show that such families determine some real 2-manifolds embbeded in the branch locus of moduli space.
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