Hilbert Functions of Chopped Ideals
Commutative Algebra
2024-12-05 v2 Algebraic Geometry
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.
Cite
@article{arxiv.2307.02560,
title = {Hilbert Functions of Chopped Ideals},
author = {Fulvio Gesmundo and Leonie Kayser and Simon Telen},
journal= {arXiv preprint arXiv:2307.02560},
year = {2024}
}
Comments
30 pages, 2 figures, comments are welcome! v2: Fixed typos thanks to referee reports. Numbering in section 2 changed slightly. To appear in J.Algebra