A new approach to Hilbert's theorem on ternary quartics

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POWERS, Victoria, Bruce REZNICK, Claus SCHEIDERER, Frank SOTTILE, 2004. A new approach to Hilbert's theorem on ternary quartics. In: Comptes Rendus Mathematique. 339(9), pp. 617-620. ISSN 1631-073X

@article{Powers2004appro-23506, title={A new approach to Hilbert's theorem on ternary quartics}, year={2004}, doi={10.1016/j.crma.2004.09.014}, 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} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/23506"> <dc:creator>Powers, Victoria</dc:creator> <dcterms:alternative>Une nouvelle approche du théorème de Hilbert sur les quartiques ternaires</dcterms:alternative> <dc:contributor>Scheiderer, Claus</dc:contributor> <dc:creator>Sottile, Frank</dc:creator> <dc:language>eng</dc:language> <dcterms:title>A new approach to Hilbert's theorem on ternary quartics</dcterms:title> <dc:rights>deposit-license</dc:rights> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-06-04T10:16:11Z</dcterms:available> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/23506"/> <dc:creator>Reznick, Bruce</dc:creator> <dcterms:issued>2004</dcterms:issued> <dc:creator>Scheiderer, Claus</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-06-04T10:16:11Z</dc:date> <dc:contributor>Powers, Victoria</dc:contributor> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dc:contributor>Reznick, Bruce</dc:contributor> <dcterms:bibliographicCitation>Comptes Rendus Mathematique ; 339 (2004), 9. - S. 617-620</dcterms:bibliographicCitation> <dc:contributor>Sottile, Frank</dc:contributor> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> </rdf:Description> </rdf:RDF>

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