Cubic differential forms and the group law on the Jacobian of a real algebraic curve
Bollettino dell'Unione Matematica Italiana (2003)
- Volume: 6-B, Issue: 3, page 597-604
- ISSN: 0392-4041
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topHuisman, J.. "Cubic differential forms and the group law on the Jacobian of a real algebraic curve." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 597-604. <http://eudml.org/doc/196220>.
@article{Huisman2003,
abstract = {In an earlier paper [6], we gave an explicit geometric description of the group law on the neutral component of the set of real points of the Jacobian of a smooth quartic curve. Here, we generalize this description to curves of higher genus. We get a description of the group law on the neutral component of the set of real points of the Jacobian of a smooth curve in terms of cubic differential forms. When applied to canonical curves, one gets an explicit geometric description of this group law by intersecting the curve with cubic hypersurfaces.},
author = {Huisman, J.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {597-604},
publisher = {Unione Matematica Italiana},
title = {Cubic differential forms and the group law on the Jacobian of a real algebraic curve},
url = {http://eudml.org/doc/196220},
volume = {6-B},
year = {2003},
}
TY - JOUR
AU - Huisman, J.
TI - Cubic differential forms and the group law on the Jacobian of a real algebraic curve
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 597
EP - 604
AB - In an earlier paper [6], we gave an explicit geometric description of the group law on the neutral component of the set of real points of the Jacobian of a smooth quartic curve. Here, we generalize this description to curves of higher genus. We get a description of the group law on the neutral component of the set of real points of the Jacobian of a smooth curve in terms of cubic differential forms. When applied to canonical curves, one gets an explicit geometric description of this group law by intersecting the curve with cubic hypersurfaces.
LA - eng
UR - http://eudml.org/doc/196220
ER -
References
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- FICHOU, G.- HUISMAN, J., A geometric description of the neutral component of the Jacobian of a real plane curve having many pseudo-lines, Math. Nachr., 254-255 (2003), 126-131. Zbl1033.14018MR1983960
- HARNACK, A., Über die Vieltheiligkeit der ebenen algebraischen Curven, Math. Ann., 10 (1876), 189-198. MR1509883JFM08.0317.04
- HUISMAN, J., Nonspecial divisors on real algebraic curves and embeddings into real projective spaces, Ann. Mat. Pura Appl. (4), 182 (2003), 21-35. Zbl1072.14072MR1969741
- HUISMAN, J., On the neutral component of the Jacobian of a real algebraic curve having many components, Indag. Math. (N. S.) 12(1) (2001), 73-81. Zbl1014.14027MR1908140
- HUISMAN, J., A group law on smooth real quartics having at least real branches, J. Théor. Nombres Bordeaux, 14 (2002), 249-256. Zbl1019.14014MR1926001
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