Higher Du Bois and Higher Rational Pairs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915851516510208 |
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| author | Ning, Haoming Nugent, Brian |
| author_facet | Ning, Haoming Nugent, Brian |
| contents | We extend the notions of higher Du Bois and higher rational singularities to pairs in the sense of the minimal model program. We extend numerous results to these higher pairs, including Bertini type theorems, stability under finite maps and that m-rational pairs are m-Du Bois. We prove these using a generalized Kovács-Schwede-type injectivity theorem for pairs, the main technical result of this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Du Bois and Higher Rational Pairs Ning, Haoming Nugent, Brian Algebraic Geometry 14B05 (Primary) 14J17 (Secondary) We extend the notions of higher Du Bois and higher rational singularities to pairs in the sense of the minimal model program. We extend numerous results to these higher pairs, including Bertini type theorems, stability under finite maps and that m-rational pairs are m-Du Bois. We prove these using a generalized Kovács-Schwede-type injectivity theorem for pairs, the main technical result of this paper. |
| title | Higher Du Bois and Higher Rational Pairs |
| topic | Algebraic Geometry 14B05 (Primary) 14J17 (Secondary) |
| url | https://arxiv.org/abs/2510.19813 |