Local cohomologies of isolated non F-rational singularities
Abstract
In this paper, we consider positively graded isolated non F-rational singularities (R,m) with d=dim R over the field K of positive characteristic. We give a representation of lower local cohomologies Him(R) (i<d) in terms of tight closure and limit closure of certain type of parameters. As an application to isolated singularities, we show a relation between non-vanishing of the tight closure of zero in the highest local cohomology (0)*Hd(R) and non-vanishing of the cohomology Hd-1m(R).
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