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2013 Voronoi tilings hidden in crystals ---the case of maximal abelian coverings---
Tadao Oda
Tohoku Math. J. (2) 65(1): 1-30 (2013). DOI: 10.2748/tmj/1365452622

Abstract

Consider a finite connected graph possibly with multiple edges and loops. In discrete geometric analysis, Kotani and Sunada constructed the crystal associated to the graph as a standard realization of the maximal abelian covering of the graph. As an application of what the author showed in an earlier paper with Seshadri as a by-product of Geometric Invariant Theory, he shows that the Voronoi tiling (also known as the Wigner-Seitz tiling) is hidden in the crystal, that is, the crystal does not intrude the interiors of the top-dimensional Voronoi cells. The result turns out to be closely related to the tropical Abel-Jacobi map of the associated compact tropical curve.

Citation

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Tadao Oda. "Voronoi tilings hidden in crystals ---the case of maximal abelian coverings---." Tohoku Math. J. (2) 65 (1) 1 - 30, 2013. https://doi.org/10.2748/tmj/1365452622

Information

Published: 2013
First available in Project Euclid: 8 April 2013

zbMATH: 1264.05106
MathSciNet: MR3049637
Digital Object Identifier: 10.2748/tmj/1365452622

Subjects:
Primary: 52C22
Secondary: 05C40, 14M25, 14T05, 74E15, 82B20, 82D25

Rights: Copyright © 2013 Tohoku University

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Vol.65 • No. 1 • 2013
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