Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Uniform bounds on multigraded regularity


Authors: Diane Maclagan and Gregory G. Smith
Journal: J. Algebraic Geom. 14 (2005), 137-164
DOI: https://doi.org/10.1090/S1056-3911-04-00385-6
Published electronically: July 20, 2004
MathSciNet review: 2092129
Full-text PDF

Abstract | References | Additional Information

Abstract: We give an effective uniform bound on the multigraded regularity of a subscheme of a smooth projective toric variety $X$ with a given multigraded Hilbert polynomial. To establish this bound, we introduce a new combinatorial tool, called a Stanley filtration, for studying monomial ideals in the homogeneous coordinate ring of $X$. As a special case, we obtain a new proof of Gotzmann's regularity theorem. We also discuss applications of this bound to the construction of multigraded Hilbert schemes.


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


Additional Information

Diane Maclagan
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Address at time of publication: Department of Mathematics, Rutgers University, Hill Center-Busch Campus, Piscataway, New Jersey 08854
Email: maclagan@math.stanford.edu

Gregory G. Smith
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: ggsmith@mast.queensu.ca

DOI: https://doi.org/10.1090/S1056-3911-04-00385-6
Received by editor(s): May 14, 2003
Received by editor(s) in revised form: December 31, 2003
Published electronically: July 20, 2004
Additional Notes: Both authors were partially supported by the Mathematical Sciences Research Institute in Berkeley, California

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website