A note on Castelnuovo-Mumford regularity and Hilbert coefficients
Le Xuan Dung, Le Tuan Hoa
TL;DR
This paper establishes new bounds on Castelnuovo-Mumford regularity using Hilbert coefficients, demonstrating their near-sharpness through illustrative examples.
Contribution
It introduces novel upper and lower bounds relating Castelnuovo-Mumford regularity to Hilbert coefficients, with evidence of their effectiveness.
Findings
Bounds are nearly sharp, as shown by examples.
New relationships between regularity and Hilbert coefficients.
Enhanced understanding of algebraic invariants.
Abstract
New upper and lower bounds on the Castelnuovo-Mumford regularity are given in terms of the Hilbert coefficients. Examples are provided to show that these bounds are in some sense nearly sharp.
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