Publikation: A new approach to Hilbert's theorem on ternary quartics
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2004
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Titel in einer weiteren Sprache
Une nouvelle approche du théorème de Hilbert sur les quartiques ternaires
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Comptes Rendus Mathematique. 2004, 339(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014
Zusammenfassung
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.
Zusammenfassung in einer weiteren Sprache
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.
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510 Mathematik
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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. 2004, 339(9), pp. 617-620. ISSN 1631-073X. Available under: doi: 10.1016/j.crma.2004.09.014BibTex
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title={A new approach to Hilbert's theorem on ternary quartics},
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