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Maclagan, Diane and Yu, Josephine (2022) Higher connectivity of tropicalizations. Mathematische Annalen, 384 . pp. 1-14. doi:10.1007/s00208-021-02281-9 ISSN 0025-5831.
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Official URL: https://doi.org/10.1007/s00208-021-02281-9
Abstract
We show that the tropicalization of an irreducible d-dimensional variety over a field of characteristic 0 is (d−ℓ)-connected through codimension one, where ℓ is the dimension of the lineality space of the tropicalization. From this we obtain a higher connectivity result for skeleta of rational polytopes. We also prove a tropical analogue of the Bertini Theorem: the intersection of the tropicalization of an irreducible variety with a generic hyperplane is again the tropicalization of an irreducible variety.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Tropical geometry, Geometry, Algebraic | |||||||||||||||
| Journal or Publication Title: | Mathematische Annalen | |||||||||||||||
| Publisher: | Springer Verlag | |||||||||||||||
| ISSN: | 0025-5831 | |||||||||||||||
| Official Date: | October 2022 | |||||||||||||||
| Dates: |
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| Volume: | 384 | |||||||||||||||
| Page Range: | pp. 1-14 | |||||||||||||||
| DOI: | 10.1007/s00208-021-02281-9 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||
| Date of first compliant deposit: | 13 October 2021 | |||||||||||||||
| Date of first compliant Open Access: | 1 November 2021 | |||||||||||||||
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