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Compactness criteria for real algebraic sets and Newton polyhedra

  • Phu Phat Pham und Tien Son Pham ORCID logo EMAIL logo
Veröffentlicht/Copyright: 30. Juni 2018

Abstract

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).

MSC 2010: 14P25

Communicated by Jan Bruinier


Funding statement: 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.

Acknowledgements

The authors thank Si Tiep Dinh for useful discussions during the preparation of this paper.

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Received: 2017-05-11
Revised: 2017-12-17
Published Online: 2018-06-30
Published in Print: 2018-11-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 7.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2017-0105/pdf
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