On bounds for cohomological Hilbert functions
type: Item
instance of: scholarly article
title: On bounds for cohomological Hilbert functions
zbMATH Open document ID: 0757.13004
DOI: 10.1016/S0021-8693(05)80058-4
author: Uwe Nagel
published in: Journal of Algebra
publication date: 1992-09-27T00:00:00Z
review text: 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 \[ \text{degree-codimension}+1. \]
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14B15
zbMATH DE Number: 63903
zbMATH Keywords: Hilbert functions
zbMATH Keywords: local cohomology
zbMATH Keywords: graded module
zbMATH Keywords: Castelnuovo regularity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 63903