Uniform bounds on multigraded regularity
نویسندگان
چکیده
منابع مشابه
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 the...
متن کامل1 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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We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...
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The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study connections between two recent definitions of multigraded regularity with a view towards a better understanding of the multigraded Hilbert function of fat point schemes in P1 × · · · × Pk . MSC 2000: 13D02, ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2005
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-04-00385-6