Uniform bounds on multigraded regularity

Maclagan, Diane; Smith, Gregory

doi:10.1090/S1056-3911-04-00385-6

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
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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.

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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
MR Author ID: 607134
Email: maclagan@math.stanford.edu

Gregory G. Smith
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
MR Author ID: 622959
Email: ggsmith@mast.queensu.ca

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