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Regularity, partial elimination ideals and the canonical bundle


Author: Matthew G. Jones
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1531-1541
MSC (2000): Primary 51N15
DOI: https://doi.org/10.1090/S0002-9939-03-07389-1
Published electronically: December 23, 2003
MathSciNet review: 2053362
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Abstract: We present partial elimination ideals, which set-theoretically cut out the multiple point loci of a generic projection of a projective variety, as a way to bound the regularity of a variety in projective space. To do this, we utilize a combination of initial ideal methods and geometric methods. We first define partial elimination ideals and establish through initial ideal methods the way in which, for a given ideal, the regularity of the partial elimination ideals bounds the regularity of the given ideal. Then we explore the partial elimination ideals as a way to compute the canonical bundle of the generic projection of a variety and the canonical bundles of the multiple point loci of the projection, and we use Kodaira Vanishing to bound the regularity of the partial elimination ideals.


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Additional Information

Matthew G. Jones
Affiliation: Department of Mathematics, California State University, Dominguez Hills, 1000 E. Victoria St., Carson, California 90747
Email: mjones@csudh.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07389-1
Received by editor(s): October 5, 2001
Received by editor(s) in revised form: January 22, 2003
Published electronically: December 23, 2003
Additional Notes: The bulk of this work was completed under the direction of Mark Green as part of my Ph.D. thesis at UCLA. I am very grateful to Professor Green for all his guidance, the time and energy he devoted to me and the knowledge he imparted upon me. I am also grateful to the UCLA Mathematics Department for its support
Communicated by: Michael Stillman
Article copyright: © Copyright 2003 American Mathematical Society

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