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 language | English (US) |
|---|---|
| Pages (from-to) | 304-315 |
| Number of pages | 12 |
| Journal | Journal of Number Theory |
| Volume | 90 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2001 |
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ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
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 journal › Article
}
TY - JOUR
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.
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 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035192149&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035192149&partnerID=8YFLogxK
U2 - 10.1006/jnth.2000.2632
DO - 10.1006/jnth.2000.2632
M3 - Article
AN - SCOPUS:0035192149
VL - 90
SP - 304
EP - 315
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 2
ER -