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Matrix classes realized by automorphisms of compact Riemann surfaces of genus two. (English) Zbl 1254.57017

It is known that if \(S\) is a compact Riemann surface of genus \(g > 1\) with (conformal) automorphism group \(G\), then there exists a faithful group homomorphism from \(G =\) Aut\((S)\) into the symplectic group Sp\({}_{2g}({\mathbb Z})\), given by the natural action of \(G\) as a group of automorphisms of the first homology group \(H_1(S,{\mathbb Z})\). In this paper, which in some sense is a sequel to a 1997 paper by D. Sjerve and the author [J. Algebra 195, No. 2, 580–603 (1997; Zbl 0888.20024)], a complete list is given of representatives of all conjugacy classes of torsion elements in Sp\({}_4({\mathbb Z})\) that can occur as images of elements of \(G\) under such a monomorphism in the case \(g = 2\). The motivation for doing this is not entirely clear, but the paper appears to be correct and well written.

MSC:

57M60 Group actions on manifolds and cell complexes in low dimensions
20G99 Linear algebraic groups and related topics
30F10 Compact Riemann surfaces and uniformization

Citations:

Zbl 0888.20024
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References:

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