Generic initial ideals of points and curves

Details Generic initial ideals of points and curves Generic initial ideals of points and curves

2004-02-26

arxiv.org/abs/math/0402418v2

J. Symbolic Comput. 40 (2005), no. 3, 1023-1038

Mathematics

Commutative Algebra

AMS Latex, 20 pages, v2: 19 pages, updated references, minor corrections, proofs of some elementary facts shortened or removed

Scientific paper

10.1016/j.jsc.2005.01.009

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.

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