References & Citations
Mathematics > Algebraic Geometry
Title: Rational singularities and $q$-birational morphism
(Submitted on 11 Jan 2023 (v1), last revised 27 Mar 2024 (this version, v4))
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.
Submission history
From: Donghyeon Kim [view email][v1] Wed, 11 Jan 2023 02:00:34 GMT (19kb)
[v2] Wed, 8 Mar 2023 13:21:56 GMT (20kb)
[v3] Mon, 23 Oct 2023 09:43:27 GMT (21kb)
[v4] Wed, 27 Mar 2024 08:56:18 GMT (24kb)
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