Efficient construction of local parameters for irreducible components of an algebraic variety in nonzero characteristic

Abstract

Consider an (n-s)-dimensional algebraic variety W defined over an infinite field k of nonzero characteristic p and irreducible over this field. Let W be a subvariety of the projective space of dimension n. We prove that the local ring of W has a sequence of local parameters represented by s nonhomogeneous polynomials with the product of degrees less than the degree of the variety multiplied by a constant depending on n. This allows us to prove the existence of an effective smooth cover and a smooth stratification of an algebraic variety in the case of the ground field of nonzero characteristic, extending the analogous results of the author obtained earlier for the ground field of zero characteristic. Bibliography: 6 titles.