Abelian functions for cyclic trigonal curves of genus 4

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

doi:10.1016/j.geomphys.2007.12.001

Abelian functions for cyclic trigonal curves of genus 4

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

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36 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 language	English
Pages (from-to)	450-467
Number of pages	18
Journal	Journal of Geometry and Physics
Volume	58
Issue number	4
DOIs	https://doi.org/10.1016/j.geomphys.2007.12.001
Publication status	Published - Apr 2008

Keywords

Abelian functions
Algebraic geometry
Cyclic trigonal curve
Kleinian sigma functions

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10.1016/j.geomphys.2007.12.001

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title = "Abelian functions for cyclic trigonal curves of genus 4",

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. {\textcopyright} 2008 Elsevier Ltd. All rights reserved.",

keywords = "Abelian functions, Algebraic geometry, Cyclic trigonal curve, Kleinian sigma functions",

author = "S. Baldwin and Eilbeck, \{J. C.\} and J. Gibbons and Y. {\^O}nishi",

year = "2008",

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doi = "10.1016/j.geomphys.2007.12.001",

language = "English",

volume = "58",

pages = "450--467",

journal = "Journal of Geometry and Physics",

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publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Abelian functions for cyclic trigonal curves of genus 4

AU - Baldwin, S.

AU - Eilbeck, J. C.

AU - Gibbons, J.

AU - Ônishi, Y.

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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.

KW - Abelian functions

KW - Algebraic geometry

KW - Cyclic trigonal curve

KW - Kleinian sigma functions

UR - https://www.scopus.com/pages/publications/40849083583

U2 - 10.1016/j.geomphys.2007.12.001

DO - 10.1016/j.geomphys.2007.12.001

M3 - Article

SN - 0393-0440

VL - 58

SP - 450

EP - 467

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 4

ER -

Abelian functions for cyclic trigonal curves of genus 4

Abstract

Keywords

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