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Selected Works of S. Allen Broughton
Article
Superelliptic surfaces as p-gonal surfaces
Contemporary Mathematics (2014)
  • Sean A Broughton
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Abstract
In this brief, expository paper, we discuss superelliptic surfaces
and p-gonal surfaces, which generalize hyperelliptic surfaces. A superelliptic
surface, or more generally, a p-gonal surface, has a conformal automorphism
w of prime order such that S/<w> has genus zero. Alternatively, the surface
has an equation of the form y^p = f(x) for some rational function f(x). We
discuss normal forms, automorphism groups, and families of p-gonal surfaces.
Keywords
  • Riemann surface,
  • superelliptic surface,
  • hyperelliptic surface,
  • p-gonal
Disciplines
Publication Date
2014
DOI
http://dx.doi.org/10.1090/conm/629/12570
Citation Information
Sean A Broughton. "Superelliptic surfaces as p-gonal surfaces" Contemporary Mathematics Vol. 629 (2014) p. 15 - 28 ISSN: 0271-4132
Available at: http://works.bepress.com/allen_broughton/44/