On automorphisms groups of cyclic p -gonal Riemann surfaces

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.

On the group algebra decomposition of a Jacobian variety

“…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.…”

“…(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.…”

“…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)…”

One-dimensional families of Riemann surfaces of genus g with $$4\text {g}+4$$ 4 g + 4 automorphims

“…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.…”

Automorphism groups of cyclic p-gonal pseudo-real Riemann surfaces

“…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].…”