An analytic approach to the degree bound in the Nullstellensatz

Kwon, Hyun-Kyoung; Netyanun, Anupan; Trent, Tavan

doi:10.1090/proc/12781

An analytic approach to the degree bound in the Nullstellensatz
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by Hyun-Kyoung Kwon, Anupan Netyanun and Tavan T. Trent

Proc. Amer. Math. Soc. 144 (2016), 1145-1152

DOI: https://doi.org/10.1090/proc/12781

Published electronically: October 20, 2015

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Abstract:

The Bezout version of Hilbert’s Nullstellensatz states that polynomials without a common zero form the unit ideal. In this paper, we start with a finite number of univariate polynomials and consider the polynomials that show up as a result of the Nullstellensatz. We present a simple analytic method of obtaining a bound for the degrees of these polynomials. Our result recovers W. D. Brownawell’s bound and is consistent with that of J. Kollár in the univariate case. The proof involves some well-known results on the analyticity of complex-valued functions.

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