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Forum Mathematicum

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Volume 30, Issue 6


Compactness criteria for real algebraic sets and Newton polyhedra

Phu Phat Pham / Tien Son PhamORCID iD: http://orcid.org/0000-0003-3368-304X
  • Corresponding author
  • Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University; and Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • orcid.org/0000-0003-3368-304X
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Published Online: 2018-06-30 | DOI: https://doi.org/10.1515/forum-2017-0105


Let f:n be a polynomial and 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 𝒵(f). From this we derive necessary and sufficient criteria for the stable compactness of 𝒵(f).

Keywords: Compact; Newton polyhedra; polynomials; real algebraic sets; stable compactness

MSC 2010: 14P25


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About the article

Received: 2017-05-11

Revised: 2017-12-17

Published Online: 2018-06-30

Published in Print: 2018-11-01

The authors were partially supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED), Grant 101.04-2016.05. The second author wishes to thank Jean Bernard Lasserre for inviting him to visit the LAAS–CNRS (Toulouse) in April 2017, where the final version of this paper was completed; this visiting was supported by the European Research Council (ERC) through the ERC-Advanced Grant TAMING 666981.

Citation Information: Forum Mathematicum, Volume 30, Issue 6, Pages 1387–1395, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0105.

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