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Uniform bounds on multigraded regularity

Diane Maclagan·Gregory G. Smith
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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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Diane Maclagan, Gregory G. Smith. 2003-05-15. Uniform bounds on multigraded regularity. https://arxiv.org/abs/math/0305215

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