2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122125In 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.Final version to appear in J. Algebra; 24 pagesCommutative AlgebraAlgebraic Geometry13D02, 13D45, 14B15, 14F17text