Homeomorphism type of the non-negative part of a complete toric variety

Abstract

In this note we show that the nonnegative part of a proper complex toric variety has the homeomorphism type of a sphere, and consequently that the nonnegative part has a natural structure of a cell complex. This extends previous results of Ehlers and Jurkiewicz. The proof also provides a simplicial decomposition of the nonnegative part, and a parameterization of each maximal simplex.

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