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MiS Preprint
7/2023

Hilbert Functions of Chopped Ideals

Fulvio Gesmundo, Leonie Kayser and Simon Telen

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.

Received:
Jul 7, 2023
Published:
Jul 7, 2023
MSC Codes:
13D02, 13C40, 14N07, 65Y20
Keywords:
Hilbert function, Hilbert regularity, syzygy, liaison, tensor decomposition

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Preprint
2023 Repository Open Access
Fulvio Gesmundo, Leonie Kayser and Simon Telen

Hilbert functions of chopped ideals