Mathematics – Algebraic Geometry
Scientific paper
2003-05-15
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.
Maclagan Diane
Smith Gregory G.
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