On the mirrors of low-degree del Pezzo surfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909661706321920 |
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| author | Gugiatti, Giulia Rota, Franco |
| author_facet | Gugiatti, Giulia Rota, Franco |
| contents | We compare different constructions of mirrors of del Pezzo surfaces, focusing on degree $d \leq 3$. In particular, we extract Lefschetz fibrations, with associated exceptional collections, from the mirrors obtained via the Hori-Vafa and Fanosearch program constructions, which we relate to one another. We show with geometric methods that the Lefschetz fibrations define categorical mirrors. With a more explicit approach, we give a sequence of (numerical) mutations relating the exceptional collections considered by Auroux, Katzarkov, and Orlov with those arising in this paper. This uses the theory of surface-like pseudolattices, and extends some of the string junction results of Grassi, Halverson and Shaneson. Our argument lifts directly to an equivalence of certain Fukaya-Seidel categories arising from our fibrations and those of Auroux, Katzarkov, and Orlov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the mirrors of low-degree del Pezzo surfaces Gugiatti, Giulia Rota, Franco Algebraic Geometry High Energy Physics - Theory Symplectic Geometry 14J33, 53D37, 14F08, 14J45, 14J27, 14J17 We compare different constructions of mirrors of del Pezzo surfaces, focusing on degree $d \leq 3$. In particular, we extract Lefschetz fibrations, with associated exceptional collections, from the mirrors obtained via the Hori-Vafa and Fanosearch program constructions, which we relate to one another. We show with geometric methods that the Lefschetz fibrations define categorical mirrors. With a more explicit approach, we give a sequence of (numerical) mutations relating the exceptional collections considered by Auroux, Katzarkov, and Orlov with those arising in this paper. This uses the theory of surface-like pseudolattices, and extends some of the string junction results of Grassi, Halverson and Shaneson. Our argument lifts directly to an equivalence of certain Fukaya-Seidel categories arising from our fibrations and those of Auroux, Katzarkov, and Orlov. |
| title | On the mirrors of low-degree del Pezzo surfaces |
| topic | Algebraic Geometry High Energy Physics - Theory Symplectic Geometry 14J33, 53D37, 14F08, 14J45, 14J27, 14J17 |
| url | https://arxiv.org/abs/2506.21758 |