A New Proof of Hilbert's Theorem on Ternary Quartics
Algebraic Geometry
2010-03-29 v1
Abstract
David 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 complex 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.
Keywords
Cite
@article{arxiv.math/0405475,
title = {A New Proof of Hilbert's Theorem on Ternary Quartics},
author = {Victoria Powers and Bruce Reznick and Claus Scheiderer and Frank Sottile},
journal= {arXiv preprint arXiv:math/0405475},
year = {2010}
}
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4 pages