Small modifications of Mori dream spaces arising from ${\mathbb C}^*$-actions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912150842245120 |
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| author | Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. |
| author_facet | Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. |
| contents | We link small modifications of projective varieties with a ${\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Białynicki-Birula cells, we produce a system of birational equivariant modifications of the original variety, which includes those on which a quotient map extends from a set of semistable points to a regular morphism.
The structure of the modifications is completely described for the blowup along the sink and the source of smooth varieties with Picard number one with a ${\mathbb C}^*$-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a ${\mathbb C}^*$-action associated to short grading of their Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_07209 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Small modifications of Mori dream spaces arising from ${\mathbb C}^*$-actions Occhetta, Gianluca Romano, Eleonora A. Conde, Luis E. Solá Wiśniewski, Jarosław A. Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17 We link small modifications of projective varieties with a ${\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Białynicki-Birula cells, we produce a system of birational equivariant modifications of the original variety, which includes those on which a quotient map extends from a set of semistable points to a regular morphism. The structure of the modifications is completely described for the blowup along the sink and the source of smooth varieties with Picard number one with a ${\mathbb C}^*$-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a ${\mathbb C}^*$-action associated to short grading of their Lie algebras. |
| title | Small modifications of Mori dream spaces arising from ${\mathbb C}^*$-actions |
| topic | Algebraic Geometry Primary 14L30, Secondary 14E30, 14L24, 14M17 |
| url | https://arxiv.org/abs/2103.07209 |