K-polystability of Fano 4-folds with large Lefschetz defect
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914198575906816 |
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| author | Romano, Eleonora A. Secci, Saverio A. |
| author_facet | Romano, Eleonora A. Secci, Saverio A. |
| contents | In this paper, we investigate K-polystability on smooth complex Fano 4-folds with Lefschetz defect at least 2, focusing on the case of Lefschetz defect 3 and on Casagrande-Druel Fano 4-folds with Lefschetz defect 2. We show that exactly 5 of the 19 families of Fano 4-folds with Lefschetz defect 3 are K-polystable. Moreover, among 175 families of Casagrande-Druel Fano 4-folds with Lefschetz defect 2, we prove that 5 are K-polystable, while 132 are K-unstable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-polystability of Fano 4-folds with large Lefschetz defect Romano, Eleonora A. Secci, Saverio A. Algebraic Geometry Differential Geometry 14J45, 14J35, 32Q20 In this paper, we investigate K-polystability on smooth complex Fano 4-folds with Lefschetz defect at least 2, focusing on the case of Lefschetz defect 3 and on Casagrande-Druel Fano 4-folds with Lefschetz defect 2. We show that exactly 5 of the 19 families of Fano 4-folds with Lefschetz defect 3 are K-polystable. Moreover, among 175 families of Casagrande-Druel Fano 4-folds with Lefschetz defect 2, we prove that 5 are K-polystable, while 132 are K-unstable. |
| title | K-polystability of Fano 4-folds with large Lefschetz defect |
| topic | Algebraic Geometry Differential Geometry 14J45, 14J35, 32Q20 |
| url | https://arxiv.org/abs/2409.03571 |