Mori dream singular $K3$ surfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915075518889984 |
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| author | Laface, Antonio Massarenti, Alex Montoya, William D. |
| author_facet | Laface, Antonio Massarenti, Alex Montoya, William D. |
| contents | We take a first step towards the classification of singular Mori dream $K3$ surfaces. We prove that if the Picard lattice of a singular $K3$ surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular $K3$ surfaces, of Picard rank two, being Mori dream is equivalent to contain two negative curves intersecting each other, and apply this result to study Mori dreamness of $K3$ surfaces with a singular point of type $A_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mori dream singular $K3$ surfaces Laface, Antonio Massarenti, Alex Montoya, William D. Algebraic Geometry Number Theory Primary 14J28, 14E30, Secondary 11D09 We take a first step towards the classification of singular Mori dream $K3$ surfaces. We prove that if the Picard lattice of a singular $K3$ surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular $K3$ surfaces, of Picard rank two, being Mori dream is equivalent to contain two negative curves intersecting each other, and apply this result to study Mori dreamness of $K3$ surfaces with a singular point of type $A_n$. |
| title | Mori dream singular $K3$ surfaces |
| topic | Algebraic Geometry Number Theory Primary 14J28, 14E30, Secondary 11D09 |
| url | https://arxiv.org/abs/2412.17036 |