Upper Bounds on Resolvent Degree via Sylvester's Obliteration Algorithm

Abstract

For each $n$, let RD$(n)$ denote the minimum $d$ for which there exists a formula for the general polynomial of degree $n$ in algebraic functions of at most $d$ variables. In this paper, we recover an algorithm of Sylvester for determining non-zero solutions of systems of homogeneous polynomials, which we present from a modern algebro-geometric perspective. We then use this geometric algorithm to determine improved thresholds for upper bounds on RD$(n)$.

33 pages. Minor revisions. To appear in New York Journal of Mathematics

References in corpus (4)

• Felix Klein's "About the Solution of the General Equations of Fifth and Sixth Degree (Excerpt from a letter to Mr. K. Hensel)"
• Upper Bounds on Resolvent Degree and Its Growth Rate
• Anders Wiman's "On the Application of Tschirnhaus Transformations to the Reduction of Algebraic Equations''
• G.N. Chebotarev's "On the Problem of Resolvents"