A global lojasiewicz inequality for algebraic varieties

Shanyu Ji; János Kollár; Bernard Shiffman

doi:10.1090/S0002-9947-1992-1046016-6

A global lojasiewicz inequality for algebraic varieties

Shanyu Ji, János Kollár, Bernard Shiffman

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Abstract

Let X be the locus of common zeros of polynomials f₁,. , f_k in n complex variables. A global upper bound for the distance to X is given in the form of a Lojasiewicz inequality. The exponent in this inequality is bounded by d^min(n, k) where d = max(3, deg f_i). The estimates are also valid over an algebraically closed field of any characteristic.

Original language	English (US)
Pages (from-to)	813-818
Number of pages	6
Journal	Transactions of the American Mathematical Society
Volume	329
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1992-1046016-6
State	Published - Feb 1992
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1992-1046016-6

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title = "A global lojasiewicz inequality for algebraic varieties",

abstract = "Let X be the locus of common zeros of polynomials f1,. , fk in n complex variables. A global upper bound for the distance to X is given in the form of a Lojasiewicz inequality. The exponent in this inequality is bounded by dmin(n, k) where d = max(3, deg fi). The estimates are also valid over an algebraically closed field of any characteristic.",

author = "Shanyu Ji and J{\'a}nos Koll{\'a}r and Bernard Shiffman",

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AB - Let X be the locus of common zeros of polynomials f1,. , fk in n complex variables. A global upper bound for the distance to X is given in the form of a Lojasiewicz inequality. The exponent in this inequality is bounded by dmin(n, k) where d = max(3, deg fi). The estimates are also valid over an algebraically closed field of any characteristic.

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A global lojasiewicz inequality for algebraic varieties

Abstract

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