Core versus graded core and global sections of line bundles

Details Core versus graded core and global sections of line bundles Core versus graded core and global sections of line bundles

2003-01-17

arxiv.org/abs/math/0301190v2

Mathematics

Commutative Algebra

23 pages, latex, final version, to appear in Transactions of AMS

Scientific paper

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.

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