The stack of $G$-zips is a Mori dream space
2024
Online
report
We first extend previous results of the author with T. Wedhorn and W. Goldring regarding the existence of $\mu$-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.
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The stack of $G$-zips is a Mori dream space
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Autor/in / Beteiligte Person: | Koskivirta, Jean-Stefan |
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Veröffentlichung: | 2024 |
Medientyp: | report |
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