Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations
We show that equivariant tilting modules over equivariant algebras induce equivalences of derived factorization categories. As an application, we show that the derived category of a noncommutative resolution of a linear section of a Pfaffian variety is equivalent to the derived factorization categor...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211294 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations. Yuki Hirano. SIGMA 17 (2021), 055, 43 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862530185668067328 |
|---|---|
| author | Hirano, Yuki |
| author_facet | Hirano, Yuki |
| citation_txt | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations. Yuki Hirano. SIGMA 17 (2021), 055, 43 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that equivariant tilting modules over equivariant algebras induce equivalences of derived factorization categories. As an application, we show that the derived category of a noncommutative resolution of a linear section of a Pfaffian variety is equivalent to the derived factorization category of a noncommutative gauged Landau-Ginzburg model (Λ, χ, )ᴳᵐ, where Λ is a noncommutative resolution of the quotient singularity /GSp() arising from a certain representation of the symplectic similitude group GSp() of a symplectic vector space .
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| first_indexed | 2026-03-12T12:48:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211294 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T12:48:08Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hirano, Yuki 2025-12-29T11:04:22Z 2021 Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations. Yuki Hirano. SIGMA 17 (2021), 055, 43 pages 1815-0659 2020 Mathematics Subject Classification: 14F08; 18G80; 16E35 arXiv:2009.12785 https://nasplib.isofts.kiev.ua/handle/123456789/211294 https://doi.org/10.3842/SIGMA.2021.055 We show that equivariant tilting modules over equivariant algebras induce equivalences of derived factorization categories. As an application, we show that the derived category of a noncommutative resolution of a linear section of a Pfaffian variety is equivalent to the derived factorization category of a noncommutative gauged Landau-Ginzburg model (Λ, χ, )ᴳᵐ, where Λ is a noncommutative resolution of the quotient singularity /GSp() arising from a certain representation of the symplectic similitude group GSp() of a symplectic vector space . The author is supported by JSPS KAKENHI 19K14502. Part of this work was conducted during his stay at the Max Planck Institute for Mathematics in Bonn, from April to December 2019. The author gratefully acknowledges MPIM Bonn for their support and hospitality. Furthermore, the author would like to thank the referees for their careful reading and valuable suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations Article published earlier |
| spellingShingle | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations Hirano, Yuki |
| title | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations |
| title_full | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations |
| title_fullStr | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations |
| title_full_unstemmed | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations |
| title_short | Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations |
| title_sort | equivariant tilting modules, pfaffian varieties and noncommutative matrix factorizations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211294 |
| work_keys_str_mv | AT hiranoyuki equivarianttiltingmodulespfaffianvarietiesandnoncommutativematrixfactorizations |