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 | References | Similar Articles | Additional Information

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