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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1992-1046016-6
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.


References [Enhancements On Off] (What's this?)

  • [A] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES 36 (1969), 23-58. MR 0268188 (42:3087)
  • [BY] C. A. Berenstein and A. Yger, Bounds for the degrees in the division problem, Michigan Math. J. 37 (1990), 25-43. MR 1042512 (91c:32004)
  • [B1] W. D. Brownawell, Local diophantine Nullstellen inequalities, J. Amer. Math. Soc. 1 (1988), 311-322. MR 928261 (89h:11041)
  • [B2] -, A prime power product version of the Nullstellensatz, Michigan Math. J. (to appear).
  • [K] J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), 963-975. MR 944576 (89h:12008)
  • [L1] S. Łojasiewicz, Sur le problème de la division, Studia Math 18 (1959), 87-136. MR 0107168 (21:5893)
  • [L2] -, Ensembles semi-analytiques, IHES, Bures-sur-Yvette, 1965.
  • [M] B. Malgrange, Ideals of differentiable functions, Oxford Univ. Press, 1966. MR 0212575 (35:3446)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1046016-6
Article copyright: © Copyright 1992 American Mathematical Society

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