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.
Publié le : 2009-06-15
Classification:
Nullstellensatz,
saturated ideals,
sums of squares,
14P15,
14P99,
32B10,
11E25
@article{1255440075,
author = {Broglia
,
Fabrizio and Pieroni
,
Federica},
title = {The Nullstellensatz for real coherent analytic surfaces},
journal = {Rev. Mat. Iberoamericana},
volume = {25},
number = {1},
year = {2009},
pages = { 781-798},
language = {en},
url = {http://dml.mathdoc.fr/item/1255440075}
}
Broglia
,
Fabrizio; Pieroni
,
Federica. The Nullstellensatz for real coherent analytic surfaces. Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, pp. 781-798. http://gdmltest.u-ga.fr/item/1255440075/