Hilbert Regularity of Stanley-Reisner Rings

TL;DR

This paper characterizes the Hilbert regularity of Stanley-Reisner rings using combinatorial invariants and computes it for Gorenstein algebras, linking algebraic properties to simplicial complex data.

Contribution

It provides a new characterization of Hilbert regularity in terms of the $f$-vector and $h$-vector of simplicial complexes and extends the computation to Gorenstein algebras.

Findings

Hilbert regularity expressed via $f$-vector and $h$-vector.

Explicit computation of Hilbert regularity for Gorenstein algebras.

Connection established between algebraic regularity and combinatorial invariants.

Abstract

In this note, we characterize the Hilbert regularity of the Stanley-Reisner ring $K[\bigtriangleup]$ in terms of the $f$-vector and the $h$-vector of a simplicial complex $\bigtriangleup$. We also compute the Hilbert regularity of a Gorenstein algebra.