Investigation of rationality in two-dimensional graded rings with rational singularities, indicating conditions for their classification.
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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Kohsuke Shibata (2026) studied this question.
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