Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, I-16146 Genova, Italia
Abstract:
The reduction number of a standard graded algebra is the least integer such that there exists a minimal reduction of the homogeneous maximal ideal of such that . Vasconcelos conjectured that where is the initial ideal of an ideal in a polynomial ring with respect to a term order. The goal of this note is to prove the conjecture.