Rational singularities
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arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866914984586379264 |
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| author | Kovács, Sándor J |
| author_facet | Kovács, Sándor J |
| contents | A resolution-free definition of rational singularities is introduced, and it is proved that for a variety admitting a resolution of singularities, so in particular in characteristic zero, this is equivalent to the usual definition. It is also demonstrated that pseudo-rational singularities are rational. The main theorem, a Kempf-type criterion for rational singularities, is new even in characteristic zero contrasting an earlier result of Cutkosky that a similar result with slightly different assumptions could not hold.
Several applications are included. In particular, an Elkik-type theorem, proving that Cohen-Macaulay dlt singularities are rational in arbitrary characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_02269 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Rational singularities Kovács, Sándor J Algebraic Geometry A resolution-free definition of rational singularities is introduced, and it is proved that for a variety admitting a resolution of singularities, so in particular in characteristic zero, this is equivalent to the usual definition. It is also demonstrated that pseudo-rational singularities are rational. The main theorem, a Kempf-type criterion for rational singularities, is new even in characteristic zero contrasting an earlier result of Cutkosky that a similar result with slightly different assumptions could not hold. Several applications are included. In particular, an Elkik-type theorem, proving that Cohen-Macaulay dlt singularities are rational in arbitrary characteristic. |
| title | Rational singularities |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1703.02269 |