Multigraded regularity, a*-invariant and the minimal free resolution

Details Multigraded regularity, a*-invariant and the minimal free resolution Multigraded regularity, a*-invariant and the minimal free resolution

2005-01-26

arxiv.org/abs/math/0501479v2

Mathematics

Commutative Algebra

Final version to appear in J. Algebra; 24 pages

Scientific paper

In recent years, two different multigraded variants of Castelnuovo-Mumford regularity have been developed, namely multigraded regularity, defined by the vanishing of multigraded pieces of local cohomology modules, and the resolution regularity vector, defined by the multidegrees in a minimal free resolution. In this paper, we study the relationship between multigraded regularity and the resolution regularity vector. Our method is to investigate multigraded variants of the usual a*-invariant. This, in particular, provides an effective approach to examining the vanishing of multigraded pieces of local cohomology modules with respect to different graded irrelevant ideals.

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