Tropical ideals do not realise all Bergman fans
| dc.contributor.author | Draisma, J | |
| dc.contributor.author | Rincón, F | |
| dc.date.accessioned | 2021-08-12T09:15:48Z | |
| dc.date.available | 2021-08-12T09:15:48Z | |
| dc.date.issued | 2021-06-28 | |
| dc.identifier.issn | 2522-0144 | |
| dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/73582 | |
| dc.description.abstract | 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. | en_US |
| dc.format.extent | 44 - ? | |
| dc.publisher | Springer | en_US |
| dc.relation.ispartof | Research in the Mathematical Sciences | |
| dc.rights | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
| dc.rights | Attribution 3.0 United States | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/3.0/us/ | * |
| dc.title | Tropical ideals do not realise all Bergman fans | en_US |
| dc.type | Article | en_US |
| dc.rights.holder | © 2021, The Author(s) | |
| dc.identifier.doi | 10.1007/s40687-021-00271-6 | |
| pubs.issue | 3 | en_US |
| pubs.notes | Not known | en_US |
| pubs.volume | 8 | en_US |
| rioxxterms.funder | Default funder | en_US |
| rioxxterms.identifier.project | Default project | en_US |
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Except where otherwise noted, this item's license is described as This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
