TY - JOUR

T1 - A new approach to Hilbert's theorem on ternary quartics

AU - Powers, Victoria

AU - Reznick, Bruce

AU - Scheiderer, Claus

AU - Sottile, Frank

N1 - Funding Information:
E-mail addresses: vicki@mathcs.emory.edu (V. Powers), reznick@math.uiuc.edu (B. Reznick), claus@math.uni-duisburg.de (C. Scheiderer), sottile@math.tamu.edu (F. Sottile). 1 Supported by the USAF under DARPA/AFOSR MURI Award F49620-02-1-0325. 2 Supported by European RTN-Network HPRN-CT-2001-00271 (RAAG). 3 Supported by the Clay Mathematical Institute, NSF CAREER grant DMS-0134860, and the MSRI.

PY - 2004/11/1

Y1 - 2004/11/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.crma.2004.09.014

DO - 10.1016/j.crma.2004.09.014

M3 - Article

AN - SCOPUS:26844496857

SN - 1631-073X

VL - 339

SP - 617

EP - 620

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -