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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2004.01445 |
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| _version_ | 1866910285773668352 |
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| author | Hochenegger, Andreas Martinengo, Elena Tonini, Fabio |
| author_facet | Hochenegger, Andreas Martinengo, Elena Tonini, Fabio |
| contents | We give a proper definition of the multiplicative structure of the following rings: the Cox ring of invertible sheaves on a general algebraic stack; and the Cox ring of rank one reflexive sheaves on a normal and excellent algebraic stack. We show that such Cox rings always exist and establish their (non-)uniqueness in terms of an Ext-group. Moreover, we compare our definition with the classical construction of a Cox ring on a variety. Finally, we give an application to the theory of Mori dream stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_01445 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Cox rings of algebraic stacks Hochenegger, Andreas Martinengo, Elena Tonini, Fabio Algebraic Geometry 13A02 (Primary) 14A20, 14L24 (Secondary) We give a proper definition of the multiplicative structure of the following rings: the Cox ring of invertible sheaves on a general algebraic stack; and the Cox ring of rank one reflexive sheaves on a normal and excellent algebraic stack. We show that such Cox rings always exist and establish their (non-)uniqueness in terms of an Ext-group. Moreover, we compare our definition with the classical construction of a Cox ring on a variety. Finally, we give an application to the theory of Mori dream stacks. |
| title | Cox rings of algebraic stacks |
| topic | Algebraic Geometry 13A02 (Primary) 14A20, 14L24 (Secondary) |
| url | https://arxiv.org/abs/2004.01445 |