$F$-rationality of two-dimensional graded rings with a rational singularity
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911141669634048 |
|---|---|
| author | Shibata, Kohsuke |
| author_facet | Shibata, Kohsuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_11090 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $F$-rationality of two-dimensional graded rings with a rational singularity Shibata, Kohsuke Commutative Algebra Algebraic Geometry 13A35, 14J17, 13A02 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. |
| title | $F$-rationality of two-dimensional graded rings with a rational singularity |
| topic | Commutative Algebra Algebraic Geometry 13A35, 14J17, 13A02 |
| url | https://arxiv.org/abs/2012.11090 |