The period matrix of Bring's curve
type: Item
instance of: scholarly article
title: The period matrix of Bring's curve
zbMATH Open document ID: 0734.30036
author: Gonzalo Riera
author: Rubí E. Rodríguez
published in: Pacific Journal of Mathematics
publication date: 1992-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 4214339
zbMATH Keywords: theta functions
zbMATH Keywords: automorphisms
zbMATH Keywords: Riemann matrix
MaRDI profile type: Publication
full work available at URL: pjm.1992.154.179
OpenAlex ID: W2009078582
DOI: 10.2140/PJM.1992.154.179
description: scientific article; zbMATH DE number 4214339