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Hilbert polynomials of j-transforms
We study transformations of finite modules over Noetherian local rings that
attach to a module a graded module defined via partial systems of parameters of . Despite
the generality of the process, which are called -transforms, in
numerous cases they have interesting cohomological properties. We focus on
deriving the Hilbert functions of -transforms and studying the
significance of the vanishing of some of its coefficients.Comment: This manuscript has been submitted to a journa
Ideals generated by quadrics
Our purpose is to study the cohomological properties of the Rees algebras of
a class of ideals generated by quadrics. For all such ideals we give the precise value of depth and decide whether the
corresponding rational maps are birational. In the case of dimension , when , we give structure theorems for all ideals of
codimension minimally generated by quadrics. For
arbitrary fields , we prove a polarized version
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