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A Global Lojasiewicz Inequality for Algebraic Varieties

Shanyu Ji, Janos Kollar and Bernard Shiffman
Transactions of the American Mathematical Society
Vol. 329, No. 2 (Feb., 1992), pp. 813-818
DOI: 10.2307/2153965
Stable URL: http://www.jstor.org/stable/2153965
Page Count: 6
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A Global Lojasiewicz Inequality for Algebraic Varieties
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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, ° fi). The estimates are also valid over an algebraically closed field of any characteristic.

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