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The stack of G-zips is a Mori dream space
- Part of
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- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 19 September 2025, pp. 1-36
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- Article
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We first extend previous results of Koskivirta with Wedhorn and 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.
