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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). |
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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).
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| Acknowledgements
The second author was supported in part by the National Science Foundation under Grant No. DMS-1944862.
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| Author information
Curtis Heberle:
Department of Mathematics
Tufts University
503 Boston Avenue, Bromfield-Pearson
Medford, MA 02155, USA
curtis.heberle@tufts.edu
Alexander J. Sutherland:
Department of Mathematics
University of California at Irvine
340 Rowland Hall
Irvine, CA 92697, USA
asuther1@uci.edu
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