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
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.