### Abstract

Let X be the locus of common zeros of polynomials f_{1},. , 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) |
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Pages (from-to) | 813-818 |

Number of pages | 6 |

Journal | Transactions of the American Mathematical Society |

Volume | 329 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1992 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Ji, S., Kollár, J., & Shiffman, B. (1992). A global lojasiewicz inequality for algebraic varieties.

*Transactions of the American Mathematical Society*,*329*(2), 813-818. https://doi.org/10.1090/S0002-9947-1992-1046016-6