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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12894 |
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| _version_ | 1866913799175405568 |
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| author | Roth, Mike |
| author_facet | Roth, Mike |
| contents | 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 Čech complex for any semi-proper toric variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homeomorphism type of the non-negative part of a complete toric variety Roth, Mike Algebraic Geometry 14M25 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 Čech complex for any semi-proper toric variety. |
| title | Homeomorphism type of the non-negative part of a complete toric variety |
| topic | Algebraic Geometry 14M25 |
| url | https://arxiv.org/abs/2504.12894 |