Hilbert Functions of Chopped Ideals

Fulvio Gesmundo, Leonie Kayser, and Simon Telen

Contact the author: Please use for correspondence this email.
Submission date: 07. Jul. 2023
Pages: 31
MSC-Numbers: 13D02, 13C40, 14N07, 65Y20
Keywords and phrases: Hilbert function, Hilbert regularity, syzygy, liaison, tensor decomposition
Download full preprint: PDF (841 kB)
Link to arXiv: See the arXiv entry of this preprint.

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.