On a non-vanishing conjecture of Kawamata and the core of an ideal

By Eero Hyry, Karen E. Smith. 2003

54 citations recorded by the source corpus.

We show, under suitable hypothesis which are sharp in a 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. This generalizes the fundamental formula for the core of an integrally closed ideal in a two dimensional regular local ring due to Huneke and Swanson. We also find a generalization of this result to singular (non-regular) settings, which we show to be intimately related to the problem of finding non-zero 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 adjoint ample line bundle on a smooth variety admits a non-zero section.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/704608b65815f71db9bb50199291ea7852d77da9

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In Algebra and Number Theory

  1. Irena Swanson
  2. Craig Huneke
  3. Juan Migliore
  4. Brian Harbourne
  5. R. Mir'o-Roig

In Geometry and Topology

  1. Irena Swanson
  2. Craig Huneke
  3. Juan Migliore
  4. Brian Harbourne
  5. R. Mir'o-Roig

In Mathematical Physics

  1. Irena Swanson
  2. Craig Huneke

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