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arXiv · 2504.12894

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

Mike Roth
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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. This result is needed in arXiv:2504.12903 as part of an argument constructing a torus-stable reduced \v{C}ech complex for any semi-proper toric variety.

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Mike Roth. 2025-04-17. Homeomorphism type of the non-negative part of a complete toric variety. https://arxiv.org/abs/2504.12894

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