Free resolutions of lex-ideals over a koszul toric ring

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we study the minimal free resolution of lex-ideals over a Koszul toric ring. In particular, we study in which toric ring R all lexidealsare componentwise linear. We give a certain necessity and sufficiency condition for this property, and show that lex-ideals in a strongly Koszul toric ring are componentwise linear. In addition, it is shown that, in the toric ring arising from the Segre product 1 × ⋯ ×1, every Hilbert function of a graded ideal is attained by a lex-ideal and that lex-ideals have the greatest graded Betti numbers among all ideals having the same Hilbert function.

Original languageEnglish
Pages (from-to)857-885
Number of pages29
JournalTransactions of the American Mathematical Society
Volume363
Issue number2
DOIs
Publication statusPublished - 2011 Feb 1
Externally publishedYes

Fingerprint

Free Resolution
Ring
Hilbert Function
Graded Betti numbers
Minimal Free Resolution
Sufficiency

Keywords

  • Componentwise linear ideals
  • Free resolutions
  • Hilbert functions
  • Koszul algebras
  • Lex-ideals
  • Toric rings

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Free resolutions of lex-ideals over a koszul toric ring. / Murai, Satoshi.

In: Transactions of the American Mathematical Society, Vol. 363, No. 2, 01.02.2011, p. 857-885.

Research output: Contribution to journalArticle

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