A new approach to Hilbert's theorem on ternary quartics
| dc.contributor.author | Powers, Victoria | deu |
| dc.contributor.author | Reznick, Bruce | deu |
| dc.contributor.author | Scheiderer, Claus | |
| dc.contributor.author | Sottile, Frank | deu |
| dc.date.accessioned | 2013-06-04T10:16:11Z | deu |
| dc.date.available | 2013-06-04T10:16:11Z | deu |
| dc.date.issued | 2004 | |
| dc.description.abstract | Hilbert proved that a non-negative real quartic form f(x,y,z)f(x,y,z) is the sum of three squares of quadratic forms. We give a new proof which shows that if the plane curve Q defined by f is smooth, then f has exactly 8 such representations, up to equivalence. They correspond to those real 2-torsion points of the Jacobian of Q which are not represented by a conjugation-invariant divisor on Q. | eng |
| dc.description.version | published | |
| dc.identifier.citation | Comptes Rendus Mathematique ; 339 (2004), 9. - S. 617-620 | deu |
| dc.identifier.doi | 10.1016/j.crma.2004.09.014 | deu |
| dc.identifier.uri | http://kops.uni-konstanz.de/handle/123456789/23506 | |
| dc.language.iso | eng | deu |
| dc.legacy.dateIssued | 2013-06-04 | deu |
| dc.rights | terms-of-use | deu |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | deu |
| dc.subject.ddc | 510 | deu |
| dc.title | A new approach to Hilbert's theorem on ternary quartics | eng |
| dc.title.alternative | Une nouvelle approche du théorème de Hilbert sur les quartiques ternaires | fra |
| dc.type | JOURNAL_ARTICLE | deu |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @article{Powers2004appro-23506,
year={2004},
doi={10.1016/j.crma.2004.09.014},
title={A new approach to Hilbert's theorem on ternary quartics},
number={9},
volume={339},
issn={1631-073X},
journal={Comptes Rendus Mathematique},
pages={617--620},
author={Powers, Victoria and Reznick, Bruce and Scheiderer, Claus and Sottile, Frank}
} | |
| kops.citation.iso690 | POWERS, Victoria, Bruce REZNICK, Claus SCHEIDERER, Frank SOTTILE, 2004. A new approach to Hilbert's theorem on ternary quartics. In: Comptes Rendus Mathematique. 2004, 339(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014 | deu |
| kops.citation.iso690 | POWERS, Victoria, Bruce REZNICK, Claus SCHEIDERER, Frank SOTTILE, 2004. A new approach to Hilbert's theorem on ternary quartics. In: Comptes Rendus Mathematique. 2004, 339(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014 | eng |
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| kops.description.abstract | Hilbert a démontré qu'une forme réelle non négative f(x,y,z)f(x,y,z) de degré 4 est la somme de trois carrés de formes quadratiques. Nous donnons une nouvelle démonstration qui montre que si la courbe plane Q definie par f est non singulière, alors f a exactement 8 telles représentations, à equivalence près. Elles correspondent aux points de 2- torsion du jacobien de Q qui ne sont pas représentés par un diviseur de Q invariant par conjugaison. | fra |
| kops.flag.knbibliography | true | |
| kops.identifier.nbn | urn:nbn:de:bsz:352-235060 | deu |
| kops.sourcefield | Comptes Rendus Mathematique. 2004, <b>339</b>(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014 | deu |
| kops.sourcefield.plain | Comptes Rendus Mathematique. 2004, 339(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014 | deu |
| kops.sourcefield.plain | Comptes Rendus Mathematique. 2004, 339(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014 | eng |
| kops.submitter.email | madeline.kreissner@uni-konstanz.de | deu |
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| source.bibliographicInfo.fromPage | 617 | |
| source.bibliographicInfo.issue | 9 | |
| source.bibliographicInfo.toPage | 620 | |
| source.bibliographicInfo.volume | 339 | |
| source.identifier.issn | 1631-073X | |
| source.periodicalTitle | Comptes Rendus Mathematique |
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