Castelnuovo-Mumford regularity and reduction number of smooth monomial curves

2007/10/24 by Michael Hellus, Hellus, Michael, Lê Tuân Hoa +3
Mathematics · #13A30 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A30 #msc:13D45

paper · pdf · doi:10.48550/arxiv.0710.4376

9 pages

arxiv created 2007/10/24 · arxiv updated 2009/12/01

Abstract

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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