The period matrix of Bring's curve
Bring's curve is the only surface of genus four admitting the symmetric group \(S_ 5\) as a group of automorphisms. In this paper a representation of \(S_ 5\) as integral matrices acting on the first homology group is derived from the universal cover; using this representation there is a one complex parameter family of matrices in Siegel's upper half space invariant by \(S_ 5\). The unique Riemann matrix corresponding to Bring's curve is determined comparing two quotients of the curve. Also, Schottky's relation can be computed in terms of theta-nulls of one complex variable and vanishes exactly for the required value.
scientific article; zbMATH DE number 4214339