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February 28, 2026Journal of Algebra and Its Applications0 citations

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

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KSKohsuke ShibataTokyo Denki University

Key Points

  • To explore the conditions under which two-dimensional graded rings with rational singularities are classified as F-rational.
  • Analyzed the structure of two-dimensional graded rings
  • Examined the relationship between rational singularities and F-rationality
  • Investigated cases with small multiplicity for classification
  • Established a correlation between multiplicity and F-rationality
  • Identified specific conditions that determine when a graded ring is F-rational
  • Demonstrated that not all two-dimensional rings with rational singularities are F-rational

Abstract

It is known that a two-dimensional Formula: see text-rational ring has a rational singularity. However a two-dimensional ring with a rational singularity is not Formula: see text-rational in general. In this paper, we investigate Formula: see text-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 Formula: see text-rational.

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Cite This Study

Kohsuke Shibata (2026) studied this question.

synapsesocial.com/papers/69a287f20a974eb0d3c03c7fhttps://doi.org/10.1142/s0219498827501714
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