Work

Hilbert functions of chopped ideals

Year: 2024

Type: article

Abstract: A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The complexity of computing these points from the chopped ideal is governed by the Hilbert function and regularity. We conjecture values for these invariants and prove them in many cases. We show that our conjecture is of practical relevance for symmetric tensor decomposition.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2024.11.017

Authors: Fulvio Gesmundo, Leonie Kayser, Simon Telen

Institutions: Université de Toulouse, Institut de Mathématiques de Toulouse, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

OpenAlex ID: W4404958429

FWCI: 1.112

Cites: 36

Cited by: 1

Related to: 10