Rational singularities and q-birational morphism

2023/01/11 by Donghyeon Kim, Kim, Donghyeon · 1 citation
Mathematics · #14B05 #14E05 #14G17 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2301.04262

openalex publication_date 2023/01/11 · openalex created_date 2024/08/11 · openalex updated_date 2026/07/28

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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