Computing Convex Hulls in the Affine Building of SL_d

Leon Zhang

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Submission date: 23. Nov. 2018
Pages: 20
Bibtex
MSC-Numbers: 52, 05
Keywords and phrases: tropical geometry, convex hulls, buildings
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Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of invertible matrices over K. As a consequence, we bound the dimension of the tropical projective space needed to realize the convex hull as a tropical polytope.