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Infinite type toric varieties and Voronoi Tilings (1608.08581v1)
Published 30 Aug 2016 in math.AG
Abstract: An infinite type toric variety is a normal toric variety given by a fan with infinitely many cones. We construct examples in this paper coming from representation theory of loop groups. The fans that appear are cones on Voronoi tilings on a vector space equipped with an inner product. We also explain the affine analogue of the connection between a generic torus orbit closure in a flag variety and the closure a maximal torus in the wonderful compactification.
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