CASTELNUOVO-MUMFORD REGULARITY AND THE DISCRETENESS OF F-JUMPING COEFFICIENTS IN GRADED RINGS

摘要

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 exist 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.