A note on the multiplicity of determinantal ideals

Herzog, Huneke, and Srinivasan have conjectured that for any homogeneous k-algebra, the multiplicity is bounded above by a function of the maximal degrees of the syzygies and below by a function of the minimal degrees of the syzygies. The goal of this paper is to establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen–Macaulay algebras over a field k for k-algebras k[x1,…,xn]/I when I is a determinantal ideal of arbitrary codimension.