Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 67-87 (2006)

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Multigraded regularity: Syzygies and fat points

Jessica Sidman and Adam Van Tuyl

Department of Mathematics and Statistics, 451A Clapp Lab, Mount Holyoke College, South Hadley, MA 01075, USA, e-mail:; Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON P7B 5E1, Canada, e-mail:

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 $\mathbb{P}^{n_1} \times \cdots \times \mathbb{P}^{n_k}$. {\bf Editorial remark:} Due to a mixup of electronic files, the published version of the paper is not the final version submitted to the journal by the authors. The current second version represents the final version. It is available electronically only. The obsoleted first version, which appeared in print, is electronically archived <a href=no.1/b47h1sid.pdf>here</a>.

Keywords: multigraded regularity, points, fat points, multiprojective space

Classification (MSC2000): 13D02, 13D40, 14F17

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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.

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