Multigraded regularity: syzygies and fat points

Abstract

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 P^{n_1} x ... x P^{n_k}.

AMS LaTex, 20 pages. v2: Revised with several small corrections. Some changes in references; v3: Small changes to Prop. 2.2 and Cor. 2.3, short appendix added. To appear in Beiträge Algebra Geom

References in corpus (4)

• Homological properties of bigraded algebras
• Castelnuovo-Mumford regularity by approximation
• Dickson invariants, regularity and computation in group cohomology
• Multigraded regularity: coarsenings and resolutions

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• The Kähler Different of a Set of Points in ${\mathbb{P}}^m\times {\mathbb{P}}^n$
• Minimal free resolutions and asymptotic behavior of multigraded regularity
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