Hilbert functions of d-regular ideals

Satoshi Murai*

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

In the present paper, we characterize all possible Hilbert functions of graded ideals in a polynomial ring whose regularity is smaller than or equal to d, where d is a positive integer. In addition, we prove the following result which is a generalization of Bigatti, Hulett and Pardue's result: Let p ≥ 0 and d > 0 be integers. If the base field is a field of characteristic 0 and there is a graded ideal I whose projective dimension proj dim (I) is smaller than or equal to p and whose regularity reg (I) is smaller than or equal to d, then there exists a monomial ideal L having the maximal graded Betti numbers among graded ideals J which have the same Hilbert function as I and which satisfy proj dim (J) ≤ p and reg (J) ≤ d. We also prove the same fact for squarefree monomial ideals. The main methods for proofs are generic initial ideals and combinatorics on strongly stable ideals.

本文言語English
ページ(範囲)658-690
ページ数33
ジャーナルJournal of Algebra
317
2
DOI
出版ステータスPublished - 2007 11月 15
外部発表はい

ASJC Scopus subject areas

  • 代数と数論

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