Uniform Bounds on Multigraded Regularity
نویسنده
چکیده
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.
منابع مشابه
1 5 M ay 2 00 3 UNIFORM BOUNDS ON MULTIGRADED REGULARITY
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 theo...
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