Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: December 23, 2003
MathSciNet review: 2053362
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 51N15

Retrieve articles in all journals with MSC (2000): 51N15


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: http://dx.doi.org/10.1090/S0002-9939-03-07389-1
PII: S 0002-9939(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