Open Access
June, 2009 The Nullstellensatz for real coherent analytic surfaces
Fabrizio Broglia , Federica Pieroni
Rev. Mat. Iberoamericana 25(2): 781-798 (June, 2009).


In this paper we prove Hilbert Nullstellensatz for real coherent analytic surfaces and we give a precise description of the obstruction to get it in general. Refering the first, we prove that the ideals of global functions vanishing on analytic subsets are exactly the real saturated ones. For $\mathbb{R}^3$ we prove that the real Nullstellensatz holds for real saturated ideals if and only if no principal ideal generated by a function whose zero set is a curve (indeed, a special function) is real. This led us to compare the Nullstellensatz problem with the Hilbert 17th one, also in its weaker form involving infinite sums of squares, proving that they share in fact the same obstruction.


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Fabrizio Broglia . Federica Pieroni . "The Nullstellensatz for real coherent analytic surfaces." Rev. Mat. Iberoamericana 25 (2) 781 - 798, June, 2009.


Published: June, 2009
First available in Project Euclid: 13 October 2009

zbMATH: 1215.14058
MathSciNet: MR2569554

Primary: 14P15 , 14P99
Secondary: 11E25 , 32B10

Keywords: Nullstellensatz , saturated ideals , sums of squares

Rights: Copyright © 2009 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.25 • No. 2 • June, 2009
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