Abelian functions for cyclic trigonal curves of genus 4

S. Baldwin, J. C. Eilbeck, J. Gibbons, Y. Ônishi

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

We discuss the theory of generalized Weierstrass s and P-functions defined on a trigonal curve of genus 4, following earlier work on the genus 3 case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve y3 = x5 + ?4 x4 + ?3 x3 + ?2 x2 + ?1 x + ?0 is discussed in detail, including a list of some of the associated partial differential equations satisfied by the P-functions, and the derivation of addition formulae. © 2008 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)450-467
Number of pages18
JournalJournal of Geometry and Physics
Volume58
Issue number4
DOIs
Publication statusPublished - Apr 2008

Keywords

  • Abelian functions
  • Algebraic geometry
  • Cyclic trigonal curve
  • Kleinian sigma functions

Fingerprint Dive into the research topics of 'Abelian functions for cyclic trigonal curves of genus 4'. Together they form a unique fingerprint.

Cite this