On Mori dreamness of blowups along space curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911198206754816 |
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| author | Guerreiro, Tiago Duarte Zikas, Sokratis |
| author_facet | Guerreiro, Tiago Duarte Zikas, Sokratis |
| contents | We study the problem of determining when the blowup $X \to \mathbb{P}^3$ along a smooth space curve $C$ is a Mori Dream Space. We obtain sufficient conditions, as well obstructions to the Mori dreamness of $X$ based on the external geometry of $C$. We furthermore find infinitely many pairs $(g,d)$ such that the corresponding Hilbert schemes $H_{g,d}^S$ admit components whose general element has these obstructions. As a consequence we show that Mori dreamness is not an open property in flat families and exhibit various degenerational pathologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Mori dreamness of blowups along space curves Guerreiro, Tiago Duarte Zikas, Sokratis Algebraic Geometry 14M05, 14C05, 14H50 (Primary) 14M06, 14E30 (Secondary) We study the problem of determining when the blowup $X \to \mathbb{P}^3$ along a smooth space curve $C$ is a Mori Dream Space. We obtain sufficient conditions, as well obstructions to the Mori dreamness of $X$ based on the external geometry of $C$. We furthermore find infinitely many pairs $(g,d)$ such that the corresponding Hilbert schemes $H_{g,d}^S$ admit components whose general element has these obstructions. As a consequence we show that Mori dreamness is not an open property in flat families and exhibit various degenerational pathologies. |
| title | On Mori dreamness of blowups along space curves |
| topic | Algebraic Geometry 14M05, 14C05, 14H50 (Primary) 14M06, 14E30 (Secondary) |
| url | https://arxiv.org/abs/2509.10148 |