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Multiplicity and Castelnuovo–Mumford Regularity of Stanley–Reisner Rings
Naoki Terai, Ken-ichi Yoshida

 

Abstract

In this paper, we pose the following conjecture and give a positive answer to the case dimΔ≤2: Let Δ be a (d−1)-dimensional simplicial complex on [n]. Fix an integer with 0≤nd−1. If e(K[Δ])≤(+1)d and β ,+d (K[Δ])=0, then reg K[Δ]≤d−1. Moreover, we discuss the relationship between the above conjecture and the lower bound theorem.