On a Non-Vanishing Conjecture of Kawamata and the Core of an Ideal

2003/01/17 by Eero Hyry, Hyry, Eero, Karen E. Smith +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #math.AC #math.AG #msc:13C99 #msc:14E99

paper · pdf · doi:10.48550/arxiv.math/0301189

50 pages latex. This is essentially the same preprint which has been available on Smith's web page for the last year; only minor changes

arxiv created 2003/01/17 · arxiv updated 2009/11/30

Abstract

We show that under suitable hypothesis (which are sharp in certain sense) that the core of an m-primary ideal in a regular local ring of dimension d is equal to the adjoint (or multiplier) ideal of its d-th power, generalizing a result of Huneke and Swanson in dimension two. We also prove a version of this in the singular setting, which we show to be intimately related to the problem of finding global sections of ample line bundles on projective varieties. In particular, we show that a graded analog of our formula for core would imply a remarkable conjecture of Kawamata predicting that every ample adjoint bundle has a non-trivial section.

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• On a Grauert-Riemenschneider vanishing theorem in dimension 3
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