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arXiv · math/0301190

Core versus graded core and global sections of line bundles

Eero Hyry·Karen E. Smith
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Abstract

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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Eero Hyry, Karen E. Smith. 2003-04-21. Core versus graded core and global sections of line bundles. https://arxiv.org/abs/math/0301190

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