Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911870566268928 |
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| author | Orlov, Dmitri |
| author_facet | Orlov, Dmitri |
| contents | New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and the resulting DG algebras are smooth. This description allows us to show that some of these DG algebras determine smooth proper noncommutative curves that provide smooth minimal noncommutative resolutions for singular rational curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves Orlov, Dmitri Algebraic Geometry Category Theory Rings and Algebras 14A22, 16E45, 16P10, 16E35, 18G80 New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and the resulting DG algebras are smooth. This description allows us to show that some of these DG algebras determine smooth proper noncommutative curves that provide smooth minimal noncommutative resolutions for singular rational curves. |
| title | Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves |
| topic | Algebraic Geometry Category Theory Rings and Algebras 14A22, 16E45, 16P10, 16E35, 18G80 |
| url | https://arxiv.org/abs/2405.04738 |