A new approach to Hilbert's theorem on ternary quartics

Victoria Powers, Bruce Reznick, Claus Scheiderer, Frank Sottile

Research output: Contribution to journalArticle

Abstract

Hilbert proved that a non-negative real quartic form 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.

Original languageEnglish (US)
Pages (from-to)617-620
Number of pages4
JournalComptes Rendus Mathematique
Volume339
Issue number9
DOIs
StatePublished - Nov 1 2004

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'A new approach to Hilbert's theorem on ternary quartics'. Together they form a unique fingerprint.

  • Cite this