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 ℓ with 0≤ℓ≤n−d−1. If e(K[Δ])≤(ℓ+1)d−ℓ and βℓ,ℓ+d(K[Δ])=0, then reg K[Δ]≤d−1. Moreover, we discuss the relationship between the above conjecture and the lower bound theorem.
Original language | English |
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Pages (from-to) | 61-69 |
Number of pages | 9 |
Journal | Acta Mathematica Vietnamica |
Volume | 40 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 1 2015 |
Externally published | Yes |
Keywords
- Arithmetic degree
- Castelnuovo–Mumford regularity
- Lower bound theorem
- Multiplicity
- Stanley–Reisner ring
ASJC Scopus subject areas
- Mathematics(all)