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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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.
References
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Bibliographic Information
  • Sean Monahan
  • Affiliation: Department of Pure Mathematics, University of Waterloo, 200 University Ave. W, Waterloo, Ontario, Canada
  • ORCID: 0009-0008-3559-8336
  • Email: sean.monahan@uwaterloo.ca
  • Received by editor(s): June 22, 2023
  • Received by editor(s) in revised form: June 20, 2024
  • Published electronically: December 27, 2024
  • Additional Notes: The author was supported by a PGS-D scholarship from the Natural Sciences and Engineering Research Council of Canada (reference number: PGSD3-558713-2021).
  • © Copyright 2024 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 1167-1214
  • MSC (2020): Primary 14M27, 14A20, 05E14; Secondary 14M17, 14M15, 14M25
  • DOI: https://doi.org/10.1090/tran/9297