Images of toric variety and amplified endomorphism of weak Fano threefolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915478312583168 |
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| author | Sarkar, Supravat |
| author_facet | Sarkar, Supravat |
| contents | We show that some important classes of weak Fano $3$-folds of Picard rank $2$ do not satisfy Bott vanishing. Using this we show that any smooth projective $3$-fold $X$ of Picard rank $2$ with $-K_X$ nef which is the image of a projective toric variety is toric. This proves a special case of a conjecture by Ochetta-Wisniewski, extending a corresponding previous work for Fano $3$-folds. We also show that a weak Fano $3$-fold of Picard rank $2$ having an int-amplified endomorphism is toric. This proves a special case of a conjecture by Fakhrudding, Meng, Zhang and Zhong, extending corresponding previous work for Fano $3$-folds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Images of toric variety and amplified endomorphism of weak Fano threefolds Sarkar, Supravat Algebraic Geometry 14M25, 14E20 We show that some important classes of weak Fano $3$-folds of Picard rank $2$ do not satisfy Bott vanishing. Using this we show that any smooth projective $3$-fold $X$ of Picard rank $2$ with $-K_X$ nef which is the image of a projective toric variety is toric. This proves a special case of a conjecture by Ochetta-Wisniewski, extending a corresponding previous work for Fano $3$-folds. We also show that a weak Fano $3$-fold of Picard rank $2$ having an int-amplified endomorphism is toric. This proves a special case of a conjecture by Fakhrudding, Meng, Zhang and Zhong, extending corresponding previous work for Fano $3$-folds. |
| title | Images of toric variety and amplified endomorphism of weak Fano threefolds |
| topic | Algebraic Geometry 14M25, 14E20 |
| url | https://arxiv.org/abs/2506.16325 |