Uniform bounds on multigraded regularity

Details Uniform bounds on multigraded regularity Uniform bounds on multigraded regularity

2003-05-15

arxiv.org/abs/math/0305215v1

Journal of Algebraic Geometry, 14 (2005) 137-164.

Mathematics

Algebraic Geometry

23 pages, 2 figures

Scientific paper

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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