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Varieties of tropical ideals are balanced
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Maclagan, Diane and Rincón, Felipe (2022) Varieties of tropical ideals are balanced. Advances in Mathematics, 410 (Part A). 108713. doi:10.1016/j.aim.2022.108713 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2022.108713
Abstract
Tropical ideals, introduced in [MR18], define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of the same dimension as the ideal. This means that every subscheme of a tropical toric variety defined by a tropical ideal has an associated class in the Chow ring of the toric variety. A key tool in the proof is that specialization of variables in a tropical ideal yields another tropical ideal; this plays the role of hyperplane sections in the theory. We also show that elimination theory (projection of varieties) works for tropical ideals as in the classical case. The matroid condition that defines tropical ideals is crucial for these results
| 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, Toric varieties, Polyhedra, Combinatorial analysis | ||||||||
| Journal or Publication Title: | Advances in Mathematics | ||||||||
| Publisher: | Academic Press | ||||||||
| ISSN: | 0001-8708 | ||||||||
| Official Date: | 3 December 2022 | ||||||||
| Dates: |
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| Volume: | 410 | ||||||||
| Number: | Part A | ||||||||
| Article Number: | 108713 | ||||||||
| DOI: | 10.1016/j.aim.2022.108713 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 4 October 2022 | ||||||||
| Date of first compliant Open Access: | 6 October 2023 | ||||||||
| RIOXX Funder/Project Grant: |
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