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arXiv · 2012.11090

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

Kohsuke Shibata
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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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Kohsuke Shibata. 2020-12-21. $F$-rationality of two-dimensional graded rings with a rational singularity. https://arxiv.org/abs/2012.11090

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