2003/01/17 by Eero Hyry, Hyry, Eero, Karen E. Smith +1 · 1 citation
Mathematics · #13C99 #14E99 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13C99 #msc:14E99
paper · pdf · doi:10.48550/arxiv.math/0301190
23 pages, latex, final version, to appear in Transactions of AMS
arxiv created 2003/04/21 · arxiv updated 2009/11/30
We find formulas for the graded core of certain m-primary ideals in a graded ring. In particular, if S is the section ring of an ample line bundle on a Cohen-Macaulay complex projective variety, we show that under suitable hypothesis, the core and graded core of the ideal of S generated by all elements of degrees at least N (for some, equivalently every, large N) are equal if and only if the line bundle admits a non-zero global section. We also prove a formula for the graded core of the powers of the unique homogeneous maximal ideal in a standard graded Cohen-Macaulay ring of arbitrary characteristic. Several open problems are posed whose solutions would lead to progress on a non-vanishing conjecture of Kawamata.