Castelnuovo-Mumford regularity and the discreteness of F-jumping coefficients in graded rings

2011/10/10 by Mordechai Katzman, Katzman, Mordechai, Wenliang Zhang +1
Mathematics · #13A35 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13A35

paper · pdf · doi:10.48550/arxiv.1110.2093

Minor changes. To appear in the Transactions of the AMS

arxiv created 2012/07/12 · arxiv updated 2012/07/13

Abstract

In this paper we show that the sets of F-jumping coefficients of ideals form discrete sets in certain graded F-finite rings. We do so by giving a criterion based on linear bounds for the growth of the Castelnuovo-Mumford regularity of certain ideals. We further show that these linear bounds exists for one-dimensional rings and for ideals of (most) two-dimensional domains. We conclude by applying our technique to prove that all sets of F-jumping coefficients of all ideals in the determinantal ring given as the quotient by 2× 2 minors in a 2× 3 matrix of indeterminates form discrete sets.

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