57
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Generic Initial Ideals of Arithmetically Cohen–Macaulay Projective Subschemes

, &
Pages 2281-2297 | Received 04 Aug 2005, Published online: 11 Jun 2007
 

Abstract

For an arithmetically Cohen–Macaulay closed subscheme X in ℙ n with the saturated defining ideal I X  ⊂ k[x 0,…, x n ], let gin(I X ) be the generic initial ideal under the reverse lexicographic order. In this article, we find the minimal system of generators of gin (I X ) in terms of characters f i s, which will be defined in (Equation3.1). Then we obtain the formula for deg(X) in terms of characters. For a curve C in ℙ n , we get the formula for the arithmetic genus in terms of characters of a general hyperplane section and the number of sporadic zeros. As an application, we give a new proof of the following upper bound on the regularity given in Ahn and Migliore (Citation2007) and Nagel (Citation1989): if X ⊂ ℙ n is an arithmetically Cohen–Macaulay closed subscheme, then

where s = {l | (I X ) l  ≠ 0}. Furthermore we give an equivalent condition for an arithmetically Cohen–Macaulay closed subscheme X ⊂ ℙ n to satisfy the equality from the view point of the generic initial ideal of I X , this shows that the upper bound is sharp.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENTS

We thank the referee for the careful reading of the manuscript and many helpful remarks. The first and second authors are partially supported by BK21, and the third author is supported by National Institute for Mathematical Sciences.

Notes

Communicated by W. Bruns.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,187.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.