Castelnuovo-Mumford Regularity of the Fiber Cone for good filtrations
  In this paper we show that there is a close relationship between the invariants characterizing the homogeneous vanishing of the local cohomology of the Rees algebra and the associated graded ring for the good filtrations case. We obtain relationships between the Castelnuovo-Mumford regularity of the fiber cone, associated graded ring, Rees algebra and reduction number for the good filtrations case. 
P. H. Lima and V. H. Jorge Perez
math.AC