O Nullstellensatz efetivo

Abstract

This work, based on the paper Bounds for the degree in the Nullstellensatz, by W. Dale Brownawell, published in the Annals of Mathematics (1987), is devoted to the study of the methods used by this author to obtain an upper bound on the degrees of the coefficients in the Hilbert Nullstellensatz equation. W. Brownawell used results from the theory of transcendental numbers, complex analysis and commutative algebra and gave an upper bound for the effective Nullstellensatz, that is simply exponential in the number of variables, valid only in characteristic 0. We will explore the use of Chow forms of unmixed ideals, following the ideas of Yu. V. Nesterenko in [8] - [10], as well as the properties of resultant between two polynomials. We will nd a lower bound on the maximum modulus of a regular sequence having no common zeros and, from estimates of several complex variables, we will obtain the upper bound on the degrees of one solution.