A proof of Hilbert's theorem on ternary quartic forms with the ladder technique

TL;DR

This paper introduces a constructive proof of Hilbert's theorem on ternary quartic forms using a novel ladder technique, providing a vivid and explicit demonstration of the theorem.

Contribution

The paper presents the ladder technique as a new constructive method for proving Hilbert's theorem on ternary quartic forms.

Findings

Successful proof of Hilbert's theorem using the ladder technique

The ladder technique offers a vivid, constructive approach

Potential for broader application in algebraic geometry

Abstract

This paper proposes a totally constructive approach for the proof of Hilbert's theorem on ternary quartic forms. The main contribution is the ladder technique, with which the Hilbert's theorem is proved vividly.