Hilbert polynomials of j-transforms

Abstract

We study transformations of finite modules over Noetherian local rings that attach to a module $M$ a graded module $H_{\mathfrak{m}}^0({\mathrm{gr}}_I(M))$ defined via partial systems of parameters of $M$. Despite the generality of the process, which are called $\mathbf{j}$-transforms, in numerous cases they have interesting cohomological properties. We focus on deriving the Hilbert functions of $\mathbf{j}$-transforms and studying the significance of the vanishing of some of its coefficients.

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