Rational singularities and q-birational morphism
Abstract
In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank 1, link our notion of rational singularities with the notion of rational singularities in [Kov11], and prove generalizations of standard facts about rational singularities. Moreover, by using a definition of non-rational locus, we introduce the notion of (Bq+1) as a dual notion of well-known Serre's notion of (Sq+1), and prove a theorem about q-birational morphisms.
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