Free resolutions of lex-ideals over a koszul toric ring

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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.

元の言語English
ページ(範囲)857-885
ページ数29
ジャーナルTransactions of the American Mathematical Society
363
発行部数2
DOI
出版物ステータスPublished - 2011 2 1
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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