The stack of $G$-zips is a Mori dream space
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916126381834240 |
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| author | Koskivirta, Jean-Stefan |
| author_facet | Koskivirta, Jean-Stefan |
| contents | We first extend previous results of the author with T. Wedhorn and W. Goldring regarding the existence of $μ$-ordinary Hasse invariants for Hodge-type Shimura varieties to other automorphic line bundles. We also determine exactly which line bundles admit nonzero sections on the stack of $G$-zips of Pink--Wedhorn--Ziegler. Then, we define and study the Cox ring of the stack of $G$-zips and show that it is always finitely generated. Finally, beyond the case of line bundles, we define a ring of vector-valued automorphic forms on the stack of $G$-zips and study its properties. We prove that it is finitely generated in certain cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09852 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stack of $G$-zips is a Mori dream space Koskivirta, Jean-Stefan Number Theory Algebraic Geometry 14G35, 20G40 We first extend previous results of the author with T. Wedhorn and W. Goldring regarding the existence of $μ$-ordinary Hasse invariants for Hodge-type Shimura varieties to other automorphic line bundles. We also determine exactly which line bundles admit nonzero sections on the stack of $G$-zips of Pink--Wedhorn--Ziegler. Then, we define and study the Cox ring of the stack of $G$-zips and show that it is always finitely generated. Finally, beyond the case of line bundles, we define a ring of vector-valued automorphic forms on the stack of $G$-zips and study its properties. We prove that it is finitely generated in certain cases. |
| title | The stack of $G$-zips is a Mori dream space |
| topic | Number Theory Algebraic Geometry 14G35, 20G40 |
| url | https://arxiv.org/abs/2402.09852 |