Geometric helices on del Pezzo surfaces from tilting
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918451583385600 |
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| author | Bousseau, Pierrick |
| author_facet | Bousseau, Pierrick |
| contents | We prove that all geometric helices in the derived category of coherent sheaves on a del Pezzo surface are related by a sequence of elementary operations: rotation, shifting, orthogonal reordering, tensoring by a line bundle, and tilting. As a consequence, any two non-commutative crepant resolutions of the affine cone over a del Pezzo surface are related by mutations. The proof relies on a geometric interpretation of tilting operations as cluster transformations acting on toric models of a log Calabi--Yau surface mirror to the del Pezzo surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22065 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric helices on del Pezzo surfaces from tilting Bousseau, Pierrick Algebraic Geometry High Energy Physics - Theory Symplectic Geometry We prove that all geometric helices in the derived category of coherent sheaves on a del Pezzo surface are related by a sequence of elementary operations: rotation, shifting, orthogonal reordering, tensoring by a line bundle, and tilting. As a consequence, any two non-commutative crepant resolutions of the affine cone over a del Pezzo surface are related by mutations. The proof relies on a geometric interpretation of tilting operations as cluster transformations acting on toric models of a log Calabi--Yau surface mirror to the del Pezzo surface. |
| title | Geometric helices on del Pezzo surfaces from tilting |
| topic | Algebraic Geometry High Energy Physics - Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2603.22065 |