# Effective Nullstellensatz for arbitrary ideals

Journal of the European Mathematical Society (1999)

- Volume: 001, Issue: 3, page 313-337
- ISSN: 1435-9855

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topKollár, 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 -

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