Fano varieties with large pseudoindex and non-free rational curves
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916268187058176 |
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| author | Watanabe, Kiwamu |
| author_facet | Watanabe, Kiwamu |
| contents | For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a classification of Fano fourfolds with pseudoindex and Picard number greater than one. Combining this result with previous results, we complete the classification of smooth Fano $n$-folds with pseudoindex at least $n-2$ and Picard number greater than one. This can be seen as a generalization of various previous results. We also discuss the relations between pseudoindex and other invariants of Fano varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03438 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fano varieties with large pseudoindex and non-free rational curves Watanabe, Kiwamu Algebraic Geometry Complex Variables Differential Geometry 14J40, 14J45, 14E30 For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a classification of Fano fourfolds with pseudoindex and Picard number greater than one. Combining this result with previous results, we complete the classification of smooth Fano $n$-folds with pseudoindex at least $n-2$ and Picard number greater than one. This can be seen as a generalization of various previous results. We also discuss the relations between pseudoindex and other invariants of Fano varieties. |
| title | Fano varieties with large pseudoindex and non-free rational curves |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14J40, 14J45, 14E30 |
| url | https://arxiv.org/abs/2309.03438 |