Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals

Details Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals Finiteness of Hilbert functions and bounds for Castelnuovo-Mumford regularity of initial ideals

2006-08-04

arxiv.org/abs/math/0608118v1

Mathematics

Commutative Algebra

To appear in Trans. Amer. Math. Soc

Scientific paper

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated to reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also given for the Castelnuovo-Mumford regularity of initial ideals which depends neither on term orders nor on the coordinates, and holds for any field.

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