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Tropical schemes, tropical cycles, and valuated matroids
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Maclagan, Diane and Rincón, Felipe (2019) Tropical schemes, tropical cycles, and valuated matroids. Journal of the European Mathematical Society, 22 (3). pp. 777-796. doi:10.4171/JEMS/932 ISSN 1435-9855.
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Official URL: https://doi.org/10.4171/JEMS/932
Abstract
The tropicalization of a subvariety Y in the n-dimensional algebraic torus T is a polyhedral complex trop(Y ) that is a \combinatorial shadow" of the original variety. Some invariants of Y , such as the dimension, are encoded in trop(Y ). The complex trop(Y ) comes equipped with positive integer weights on its top-dimensional cells, called multiplicities, that make it into a tropical cycle. This extra information encodes information about the intersection theory of compacti cations of the original variety Y ; see for example [KP11].
| 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, Matroids, Vector spaces | ||||||
| Journal or Publication Title: | Journal of the European Mathematical Society | ||||||
| Publisher: | European Mathematical Society Publishing House | ||||||
| ISSN: | 1435-9855 | ||||||
| Official Date: | 19 November 2019 | ||||||
| Dates: |
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| Volume: | 22 | ||||||
| Number: | 3 | ||||||
| Page Range: | pp. 777-796 | ||||||
| DOI: | 10.4171/JEMS/932 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | To appear in Journal of the European Mathematical Society: http://www.ems-ph.org/journals/journal.php?jrn=jems © 2018 EMS Publishing House. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 11 December 2017 | ||||||
| Date of first compliant Open Access: | 26 September 2018 | ||||||
| RIOXX Funder/Project Grant: |
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