Draisma, Jan; Rincón, Felipe (2021). Tropical ideals do not realise all Bergman fans. Research in mathematical sciences, 8(3), p. 44. Springer 10.1007/s40687-021-00271-6
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Every tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Draisma, Jan |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
2522-0144 |
Publisher: |
Springer |
Funders: |
[UNSPECIFIED] Netherlands Organisation for Scientific Research ; [42] Schweizerischer Nationalfonds ; [UNSPECIFIED] Research Council of Norway |
Projects: |
[UNSPECIFIED] Vici grant Stabilisation in Algebra and Geometry
Projects 200021 not found. Projects 239968 not found. |
Language: |
English |
Submitter: |
Sebastiano Don |
Date Deposited: |
04 Feb 2022 16:15 |
Last Modified: |
05 Dec 2022 16:04 |
Publisher DOI: |
10.1007/s40687-021-00271-6 |
PubMed ID: |
34778704 |
BORIS DOI: |
10.48350/164652 |
URI: |
https://boris.unibe.ch/id/eprint/164652 |
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