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arXiv · 2309.16392

Algebraic Multiplicity and the Poincar\'{e} Problem

Jinzhi Lei·Lijun Yang
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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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Jinzhi Lei, Lijun Yang. 2023-09-28. Algebraic Multiplicity and the Poincar\'{e} Problem. https://arxiv.org/abs/2309.16392

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