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Transactions of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1046016-6
PII: S 0002-9947(1992)1046016-6
Article copyright: © Copyright 1992 American Mathematical Society