Jacobians of genus one curves

Sang Yook An, Seog Young Kim, David C. Marshall, Susan H. Marshall, William G Mccallum, Alexander R. Perlis

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1, a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve's jacobian in Weierstrass form and the covering map to its jacobian induced by the K-rational divisor at infinity. We give a unified account of all three cases.

Original languageEnglish (US)
Pages (from-to)304-315
Number of pages12
JournalJournal of Number Theory
Volume90
Issue number2
DOIs
StatePublished - 2001

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Genus
Curve
Classical Invariant Theory
Syzygy
Covering Map
Quartic
Divisor
Infinity
Cover
Form

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

An, S. Y., Kim, S. Y., Marshall, D. C., Marshall, S. H., Mccallum, W. G., & Perlis, A. R. (2001). Jacobians of genus one curves. Journal of Number Theory, 90(2), 304-315. https://doi.org/10.1006/jnth.2000.2632

Jacobians of genus one curves. / An, Sang Yook; Kim, Seog Young; Marshall, David C.; Marshall, Susan H.; Mccallum, William G; Perlis, Alexander R.

In: Journal of Number Theory, Vol. 90, No. 2, 2001, p. 304-315.

Research output: Contribution to journalArticle

An, SY, Kim, SY, Marshall, DC, Marshall, SH, Mccallum, WG & Perlis, AR 2001, 'Jacobians of genus one curves', Journal of Number Theory, vol. 90, no. 2, pp. 304-315. https://doi.org/10.1006/jnth.2000.2632
An SY, Kim SY, Marshall DC, Marshall SH, Mccallum WG, Perlis AR. Jacobians of genus one curves. Journal of Number Theory. 2001;90(2):304-315. https://doi.org/10.1006/jnth.2000.2632
An, Sang Yook ; Kim, Seog Young ; Marshall, David C. ; Marshall, Susan H. ; Mccallum, William G ; Perlis, Alexander R. / Jacobians of genus one curves. In: Journal of Number Theory. 2001 ; Vol. 90, No. 2. pp. 304-315.
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