New York Journal of Mathematics
Volume 29 (2023), 107-146


Curtis Heberle and Alexander J. Sutherland

Upper bounds on resolvent degree via Sylvester's obliteration algorithm

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Published: January 9, 2023.
Keywords: Resolvent degree, Polynomials, Rational points.
Subject [2010]: 14G25 (Primary); 12E12, 13F20 (Secondary).

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).


The second author was supported in part by the National Science Foundation under Grant No. DMS-1944862.

Author information

Curtis Heberle:
Department of Mathematics
Tufts University
503 Boston Avenue, Bromfield-Pearson
Medford, MA 02155, USA


Alexander J. Sutherland:
Department of Mathematics
University of California at Irvine
340 Rowland Hall
Irvine, CA 92697, USA