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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A global Łojasiewicz inequality for algebraic varieties

Authors: Shanyu Ji, János Kollár and Bernard Shiffman
Journal: Trans. Amer. Math. Soc. 329 (1992), 813-818
MSC: Primary 32C99; Secondary 32B99
MathSciNet review: 1046016
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Abstract: Let $ X$ be the locus of common zeros of polynomials $ {f_1}, \ldots ,{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.

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