Generic initial ideals of points and curves
摘要
Let I be the defining ideal of a smooth irreducible complete intersection space curve C with defining equations of degrees a and b. We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo-Mumford regularity 1+ab(a-1)(b-1)/2 with the exception of the case a=b=2, where the regularity is 4. Note that ab(a-1)(b-1)/2 is exactly the number of singular points of a general projection of C to the plane. Additionally, we show that for any term ordering tau, the generic initial ideal of a generic set of points in P^r is a tau-segment ideal.
引用
@article{arxiv.math/0402418,
title = {Generic initial ideals of points and curves},
author = {Aldo Conca and Jessica Sidman},
journal= {arXiv preprint arXiv:math/0402418},
year = {2012}
}
备注
AMS Latex, 20 pages, v2: 19 pages, updated references, minor corrections, proofs of some elementary facts shortened or removed. To appear in J. Symbolic Computation