Bounds for Codimensions of Fitting Ideals Original Research Article

We find upper bounds for codimensions of Fitting ideals of a module (over a regular ring), whose symmetric algebra is equidimensional. These bounds are stronger than the classical Eagon–Northcott bounds. Together with lower bounds of Simis and Vasconcelos, they show that the Fitting ideals of a module whose symmetric algebra has an irreducible spectrum can appear only in a finite number of codimensions. Our proof is based on earlier results concerning minimal primes of tensor powers of a symmetric algebra and uses one of the dimension formulæ of Huneke and Rossi.