On the Nef cones of blowups of the projective plane
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918086647480320 |
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| author | D'Urso, Luíze |
| author_facet | D'Urso, Luíze |
| contents | In this paper, we study the Cremona action on the nef cone of $S_n$, the blowup of $¶^2$ in $n$ very general points, with $n\ge9$. We construct and describe a rational polyhedral fundamental domain of the nef cone for $n=9$ with respect to this action. In the case $n\ge10$, we give a rational polyhedral fundamental domain of the $K_{S_n}$-negative part of the nef cone with respect to the Cremona action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Nef cones of blowups of the projective plane D'Urso, Luíze Algebraic Geometry Group Theory 14E30, 20F55 In this paper, we study the Cremona action on the nef cone of $S_n$, the blowup of $¶^2$ in $n$ very general points, with $n\ge9$. We construct and describe a rational polyhedral fundamental domain of the nef cone for $n=9$ with respect to this action. In the case $n\ge10$, we give a rational polyhedral fundamental domain of the $K_{S_n}$-negative part of the nef cone with respect to the Cremona action. |
| title | On the Nef cones of blowups of the projective plane |
| topic | Algebraic Geometry Group Theory 14E30, 20F55 |
| url | https://arxiv.org/abs/2412.15460 |