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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.17938 |
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| _version_ | 1866917744379691008 |
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| author | Hu, Xianyu Krah, Johannes |
| author_facet | Hu, Xianyu Krah, Johannes |
| contents | Let X be the blow-up of the projective plane in a finite set of very general points. We deduce from the work of Uehara that X has only standard autoequivalences, no nontrivial Fourier-Mukai partners, and admits no spherical objects. If X is the blow-up of the projective plane in 9 very general points, we provide an alternate and direct proof of the corresponding statement. Further, we show that the same result holds if X is a blow-up of finitely many points in a minimal surface of nonnegative Kodaira dimension which contains no (-2)-curves. Independently, we characterize spherical objects on blow-ups of minimal surfaces of positive Kodaira dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Autoequivalences of Blow-Ups of Minimal Surfaces Hu, Xianyu Krah, Johannes Algebraic Geometry 14F08, 14J26 Let X be the blow-up of the projective plane in a finite set of very general points. We deduce from the work of Uehara that X has only standard autoequivalences, no nontrivial Fourier-Mukai partners, and admits no spherical objects. If X is the blow-up of the projective plane in 9 very general points, we provide an alternate and direct proof of the corresponding statement. Further, we show that the same result holds if X is a blow-up of finitely many points in a minimal surface of nonnegative Kodaira dimension which contains no (-2)-curves. Independently, we characterize spherical objects on blow-ups of minimal surfaces of positive Kodaira dimension. |
| title | Autoequivalences of Blow-Ups of Minimal Surfaces |
| topic | Algebraic Geometry 14F08, 14J26 |
| url | https://arxiv.org/abs/2310.17938 |