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arXiv · 2301.04262

Rational singularities and $q$-birational morphism

Donghyeon Kim
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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 $(B_{q+1})$ as a dual notion of well-known Serre's notion of $(S_{q+1})$, and prove a theorem about $q$-birational morphisms.

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Donghyeon Kim. 2023-01-11. Rational singularities and $q$-birational morphism. https://doi.org/10.1142/s0129167x24500654

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