On bounds for cohomological Hilbert functions
Let \(M\) be a finitely generated graded module of Krull dimension \(n+1\) over a graded ring \(A=k[X_ 0,\dots X_ n]/I\), and let \(m=\oplus_{i>0}A_ i\). The functions \(t\mapsto\dim_ k[H^ i_ m(M)]_ t\) are studied. Some upper bounds in terms of the dimension, degree, and embedding dimension are derived, improving results earlier given by Brodman. One aim seems to be a search for a possibility to attack the conjecture of Eisenbud, that the Castelnuovo regularity is bounded by \[ \text{degree-codimension}+1. \]
scientific article; zbMATH DE number 63903
scientific article