A new phantom on a rational surface
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914147135913984 |
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| author | Ma, Shihao Xiong, Yirui Yang, Song |
| author_facet | Ma, Shihao Xiong, Yirui Yang, Song |
| contents | We construct a universal phantom subcategory on the blow-up of the complex projective plane in 11 general points. This phantom subcategory is the orthogonal complement of a non-full exceptional collection of line bundles of maximal length. It provides a new counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov. The first counterexample was constructed by Krah [Invent. Math. {\bf 235} (2024),1009--1018]. As an application, we construct a new co-connective DG-algebra whose derived category is a phantom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new phantom on a rational surface Ma, Shihao Xiong, Yirui Yang, Song Algebraic Geometry We construct a universal phantom subcategory on the blow-up of the complex projective plane in 11 general points. This phantom subcategory is the orthogonal complement of a non-full exceptional collection of line bundles of maximal length. It provides a new counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov. The first counterexample was constructed by Krah [Invent. Math. {\bf 235} (2024),1009--1018]. As an application, we construct a new co-connective DG-algebra whose derived category is a phantom. |
| title | A new phantom on a rational surface |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.07114 |