A New Proof of Hilbert's Theorem on Ternary Quartics Institutional Repository Document uri icon

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.

author list (cited authors)

  • Powers, V., Reznick, B., Scheiderer, C., & Sottile, F.

citation count

  • 0

complete list of authors

  • Powers, Victoria||Reznick, Bruce||Scheiderer, Claus||Sottile, Frank

Book Title

  • arXiv

publication date

  • May 2004