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 $k[x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n]\mathrm{/}I$ being $I$ a determinantal ideal of arbitrary codimension.