Multigraded regularity: Syzygies and fat points

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 ℙⁿ¹ × ⋯ × ℙ^nk. © 2006 Heldermann Verlag.