Loading…

On almost revlex ideals with Hilbert function of complete intersections

In this paper, we investigate the behavior of almost reverse lexicographic ideals with the Hilbert function of a complete intersection. More precisely, over a field K , we give a new constructive proof of the existence of the almost revlex ideal J ⊂ K [ x 1 , … , x n ] , with the same Hilbert functi...

Full description

Saved in:
Bibliographic Details
Published in:Ricerche di matematica 2020-06, Vol.69 (1), p.153-175
Main Authors: Bertone, Cristina, Cioffi, Francesca
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we investigate the behavior of almost reverse lexicographic ideals with the Hilbert function of a complete intersection. More precisely, over a field K , we give a new constructive proof of the existence of the almost revlex ideal J ⊂ K [ x 1 , … , x n ] , with the same Hilbert function as a complete intersection defined by n forms of degrees d 1 ≤ ⋯ ≤ d n . Properties of the reduction numbers for an almost revlex ideal have an important role in our inductive and constructive proof, which is different from the more general construction given by Pardue in 2010. We also detect several cases in which an almost revlex ideal having the same Hilbert function as a complete intersection corresponds to a singular point in a Hilbert scheme. This second result is the outcome of a more general study of lower bounds for the dimension of the tangent space to a Hilbert scheme at stable ideals, in terms of the number of minimal generators.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-019-00453-z