Jacobians of genus one curves

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

doi:10.1006/jnth.2000.2632

Jacobians of genus one curves

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

Mathematics

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P¹a 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 language	English (US)
Pages (from-to)	304-315
Number of pages	12
Journal	Journal of Number Theory
Volume	90
Issue number	2
DOIs	https://doi.org/10.1006/jnth.2000.2632
State	Published - 2001

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jnth.2000.2632

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abstract = "Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve{\textquoteright}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.",

author = "An, {Sang Yook} and Kim, {Seog Young} and Marshall, {David C.} and Marshall, {Susan H.} and McCallum, {William G.} and Perlis, {Alexander R.}",

note = "Funding Information: 1Supported by an NSF GIG grant.",

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T1 - Jacobians of genus one curves

AU - An, Sang Yook

AU - Kim, Seog Young

AU - Marshall, David C.

AU - Marshall, Susan H.

AU - McCallum, William G.

AU - Perlis, Alexander R.

N1 - Funding Information: 1Supported by an NSF GIG grant.

PY - 2001

Y1 - 2001

N2 - Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1a 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.

AB - Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P1a 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.

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U2 - 10.1006/jnth.2000.2632

DO - 10.1006/jnth.2000.2632

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JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -

Jacobians of genus one curves

Abstract

ASJC Scopus subject areas

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