Effective Nullstellensatz for arbitrary ideals

Kollár, János. "Effective Nullstellensatz for arbitrary ideals." Journal of the European Mathematical Society 001.3 (1999): 313-337. <http://eudml.org/doc/277498>.

@article{Kollár1999,
abstract = {Let $f_i$ be polynomials in $n$ variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials $g_i$ such that $\sum g_if_i=1$. The effective versions of this result bound the degrees of the $g_i$ in terms of the degrees of the $f_j$. The aim of this paper is to generalize this to the case when the $f_i$ are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.},
author = {Kollár, János},
journal = {Journal of the European Mathematical Society},
keywords = {Hilbert’s Nullstellensatz; Bézout theorem; Łojasiewicz–type inequalities; deformation theory; polynomial ideals; effectivity; Bézout theorem; Nullstellensatz; Łojasiewicz inequality},
language = {eng},
number = {3},
pages = {313-337},
publisher = {European Mathematical Society Publishing House},
title = {Effective Nullstellensatz for arbitrary ideals},
url = {http://eudml.org/doc/277498},
volume = {001},
year = {1999},
}

TY - JOUR
AU - Kollár, János
TI - Effective Nullstellensatz for arbitrary ideals
JO - Journal of the European Mathematical Society
PY - 1999
PB - European Mathematical Society Publishing House
VL - 001
IS - 3
SP - 313
EP - 337
AB - Let $f_i$ be polynomials in $n$ variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials $g_i$ such that $\sum g_if_i=1$. The effective versions of this result bound the degrees of the $g_i$ in terms of the degrees of the $f_j$. The aim of this paper is to generalize this to the case when the $f_i$ are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
LA - eng
KW - Hilbert’s Nullstellensatz; Bézout theorem; Łojasiewicz–type inequalities; deformation theory; polynomial ideals; effectivity; Bézout theorem; Nullstellensatz; Łojasiewicz inequality
UR - http://eudml.org/doc/277498
ER -