Rational singularities and $q$-birational morphism
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911259892383744 |
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| author | Kim, Donghyeon |
| author_facet | Kim, Donghyeon |
| contents | In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank $1$, link our notion of rational singularities with the notion of rational singularities in [Kov11], and prove generalizations of standard facts about rational singularities. Moreover, by using a definition of non-rational locus, we introduce the notion of $(B_{q+1})$ as a dual notion of well-known Serre's notion of $(S_{q+1})$, and prove a theorem about $q$-birational morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04262 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational singularities and $q$-birational morphism Kim, Donghyeon Algebraic Geometry 14B05, 14E05, 14G17 In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank $1$, link our notion of rational singularities with the notion of rational singularities in [Kov11], and prove generalizations of standard facts about rational singularities. Moreover, by using a definition of non-rational locus, we introduce the notion of $(B_{q+1})$ as a dual notion of well-known Serre's notion of $(S_{q+1})$, and prove a theorem about $q$-birational morphisms. |
| title | Rational singularities and $q$-birational morphism |
| topic | Algebraic Geometry 14B05, 14E05, 14G17 |
| url | https://arxiv.org/abs/2301.04262 |