Castelnuovo-Mumford regularity and reduction number of smooth monomial curves

Details Castelnuovo-Mumford regularity and reduction number of smooth monomial curves Castelnuovo-Mumford regularity and reduction number of smooth monomial curves

2007-10-24

arxiv.org/abs/0710.4376v1

Mathematics

Commutative Algebra

9 pages

Scientific paper

We compare, for smooth monomial projective curves, the Castel- nuovo-Mumford
regularity and the reduction number; we present an example where these two
numbers differ. However, we show they coin- cide for a certain class of
monomial curves. Furthermore, for smooth monomial curves we prove an inequality
which is stronger than the one from the Eisenbud-Goto conjecture.

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