Kyoto Journal of Mathematics

Spin networks, Ehrhart quasipolynomials, and combinatorics of dormant indigenous bundles

Yasuhiro Wakabayashi

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It follows from work of S. Mochizuki, F. Liu, and B. Osserman that there is a relationship between Ehrhart’s theory concerning rational polytopes and the geometry of the moduli stack classifying dormant indigenous bundles on a proper hyperbolic curve in positive characteristic. This relationship was established by considering the (finite) cardinality of the set consisting of certain colorings on a 3-regular graph called spin networks. In the present article, we recall the correspondences between spin networks, lattice points of rational polytopes, and dormant indigenous bundles and present some identities and explicit computations of invariants associated with the objects involved.

Article information

Kyoto J. Math., Volume 59, Number 3 (2019), 649-684.

Received: 6 November 2014
Revised: 5 April 2017
Accepted: 15 May 2017
First available in Project Euclid: 2 July 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 52B05: Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]

p-adic Teichmüller theory indigenous bundle p-curvature spin network Ehrhart polynomial


Wakabayashi, Yasuhiro. Spin networks, Ehrhart quasipolynomials, and combinatorics of dormant indigenous bundles. Kyoto J. Math. 59 (2019), no. 3, 649--684. doi:10.1215/21562261-2019-0020.

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