Compactness criteria for real algebraic sets and newton polyhedra

Phu-Phat Pham; Tien-Son Pham

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arXiv · 1705.10917

Compactness criteria for real algebraic sets and newton polyhedra

Phu-Phat Pham·Tien-Son Pham

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Abstract

Let $f \colon \mathbb{R}^n \rightarrow \mathbb{R}$ be a polynomial and $\mathcal{Z}(f)$ its zero set. In this paper, in terms of the so-called Newton polyhedron of $f,$ we present a necessary criterion and a sufficient condition for the compactness of $\mathcal{Z}(f).$ From this we derive necessary and sufficient criteria for the stable compactness of $\mathcal{Z}(f).$

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Phu-Phat Pham, Tien-Son Pham. 2017-05-31. Compactness criteria for real algebraic sets and newton polyhedra. https://arxiv.org/abs/1705.10917

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