$F$-rationality of two-dimensional graded rings with a rational singularity
Commutative Algebra
2025-09-09 v3 Algebraic Geometry
Abstract
It is known that a two-dimensional -rational ring has a rational singularity. However a two-dimensional ring with a rational singularity is not -rational in general. In this paper, we investigate -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 -rational.
Keywords
Cite
@article{arxiv.2012.11090,
title = {$F$-rationality of two-dimensional graded rings with a rational singularity},
author = {Kohsuke Shibata},
journal= {arXiv preprint arXiv:2012.11090},
year = {2025}
}
Comments
33 pages, I have slightly modified the proof of Theorem 4.5 and added Lemma 4.3 to support it