Mathematical Sciences Faculty Research

Article

2-21-2018

Abstract

This article generalizes joint work of the first author and I. Swanson to the s-multiplicity recently introduced by the second author. For k a field and X=[xi,j] a m×n-matrix of variables, we utilize Gröbner bases to give a closed form the length λ(k[X]/(I2(X)+m⌈sq⌉+m[q])) where s∈Z[p−1], q is a sufficiently large power of p, and m is the homogeneous maximal ideal of k[X]. This shows this length is always eventually a {\it polynomial} function of q for all s.

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