Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-12T08:34:20.431Z Has data issue: false hasContentIssue false
  • English
  • Français

Three Plane Sextics and their Automorphisms

Published online by Cambridge University Press:  20 November 2018

W. L. Edge
W. L. Edge*
Affiliation:
University of Edinburgh, Edinburgh, Scotland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. The sextics of the title have five cusps and are particular examples of the curve encountered by Humbert (5). The claim to notoriety of Humbert's curve of genus 5 has been that all its abelian integrals of the first kind are linear combinations of five elliptic integrals; it also has (1) the striking property that its 120 Weierstrassian points are confluent in threes at only 40 distinct points; whereas a general curve of genus 5 has, after Riemann, 12 moduli, a Humbert curve has merely 2. The three curves to be studied now have no free moduli at all, but although this tempts one to construct period matrices, such transcendental topics will not be handled here.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1263 - 1278
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Edge, W. L., Humbert's plane sextics of genus 5, Proc. Cambridge Philos. Soc. 47 (1951), 483–495 Google Scholar
2. Edge, W. L., A new look at the Kummer surface, Can. J. Math. 19 (1967), 952–967.Google Scholar
3. Enriques, F., Teoria geometrica delle equazioni e delle funzioni algebriche, Vol. III (Zanichelli, Bologna, 1924).Google Scholar
4. Hudson, H. P., Cremona transformations in plane and space (Cambridge, at the University Press, 1927).Google Scholar
5. Humbert, G., Sur un complex remarquable de coniques et sur la surface du troisième ordre, J. Ecole Polytechnique 64 (1894), 123–149.Google Scholar
6. Wiman, A., Über die algebraischen Curven von den Geschlechtern p = 4, 5 und 6, welche eindeutige Transformationen in sich besitzen, Svenska Vet.-Akad. Handlingar Bihang till Handlingar 21 (1895), afd. 1, no. 3, 41 pp.Google Scholar