Horospherical stacks and stacky coloured fans

Monahan, Sean

doi:10.1090/tran/9297

Horospherical stacks and stacky coloured fans
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by Sean Monahan;

Trans. Amer. Math. Soc. 378 (2025), 1167-1214

DOI: https://doi.org/10.1090/tran/9297

Published electronically: December 27, 2024

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Abstract:

We introduce a combinatorial theory of horospherical stacks which is motivated by the work of Geraschenko and Satriano on toric stacks. A horospherical stack corresponds to a combinatorial object called a stacky coloured fan. We give many concrete examples, including a class of easy-to-draw examples called coloured fantastacks. The main results in this paper are combinatorial descriptions of horospherical stacks, the morphisms between them, their decolourations, and their good moduli spaces.

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