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

Huy Tai Ha
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Abstract

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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Huy Tai Ha. 2007-01-18. Multigraded regularity, a*-invariant and the minimal free resolution. https://arxiv.org/abs/math/0501479

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