Multiplicity and Castelnuovo–Mumford Regularity of Stanley–Reisner Rings

Naoki Terai, Ken ichi Yoshida

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)61-69
Number of pages9
JournalActa Mathematica Vietnamica
Volume40
Issue number1
DOIs
Publication statusPublished - Mar 1 2015
Externally publishedYes

Keywords

  • Arithmetic degree
  • Castelnuovo–Mumford regularity
  • Lower bound theorem
  • Multiplicity
  • Stanley–Reisner ring

ASJC Scopus subject areas

  • Mathematics(all)

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