$F$-rationality of two-dimensional graded rings with a rational singularity
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.11090
- arXiv:
- arXiv:2012.11090
- Bibcode:
- 2020arXiv201211090S
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 13A35;
- 14J17;
- 13A02
- E-Print:
- 37 pages, The statement and proof of Lemma 4.4 have been corrected. The statement of Theorem 4.5 is unchanged