THE POSITIVITY OF THE FIRST COEFFICIENTS OF NORMAL HILBERT POLYNOMIALS

Abstract

Let R be an analytically unramified local ring with maximal ideal m and d = dim R > 0. If R is unmixed, then (e) over bar (1)(I)(R) >= 0 for every m-primary ideal I in R, where (e) over bar (1)(I)(R) denotes the first coefficient of the normal Hilbert polynomial of R with respect to I. Thus the positivity conjecture on (e) over bar (1)(I)(R) posed by Wolmer V. Vasconcelos is settled affirmatively.