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Algebraic Multiplicity and the Poincaré Problem

Published 28 Sep 2023 in math.CA | (2309.16392v1)

Abstract: In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the system at the singular points. A method for computing the algebraic multiplicity using Newton polygon is also presented.

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