Hilbert polynomials of j-transforms

Shiro Goto; Jooyoun Hong; Wolmer V. Vasconcelos

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arXiv · 1403.6549

Hilbert polynomials of j-transforms

Shiro Goto·Jooyoun Hong·Wolmer V. Vasconcelos

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Abstract

We study transformations of finite modules over Noetherian local rings that attach to a module $M$ a graded module $H^{0}_{\mathfrak{m}}( \mathrm{gr}_{I}(M))$ 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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Shiro Goto, Jooyoun Hong, Wolmer V. Vasconcelos. 2014-03-26. Hilbert polynomials of j-transforms. https://arxiv.org/abs/1403.6549

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