F-rationality of two-dimensional graded rings with a rational singularity

2020/12/21 by Kohsuke Shibata, Shibata, Kohsuke
Mathematics · #13A02 #13A35 #14J17 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2012.11090

openalex publication_date 2020/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that a two-dimensional F-rational ring has a rational singularity. However a two-dimensional ring with a rational singularity is not F-rational in general. In this paper, we investigate F-rationality of a two-dimensional graded ring with a rational singularity in terms of the multiplicity. Moreover, we determine when a two-dimensional graded ring with a rational singularity and a small multiplicity is F-rational.

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