Abstract
The object of this paper is to present two algebraic results with straightforward proofs, which have interesting consequences in tropical geometry. We start with an identity for polynomials over the max-plus algebra, which shows that any polynomial divides a product of binomials. Interpreted in tropical geometry, any tropical variety W can be completed to a union of tropical primitives, i.e. single-face polyhedral complexes. In certain situations, a tropical variety W has a "reversal" variety, which together with W already yields the union of primitives; this phenomenon is explained in terms of a map defined on the algebraic structure, and yields a duality on tropical hypersurfaces.
| Original language | English |
|---|---|
| Pages (from-to) | 1141-1163 |
| Number of pages | 23 |
| Journal | Journal of Algebra and its Applications |
| Volume | 10 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 2011 |
Bibliographical note
Funding Information:The research of the authors is supported by the Israel Science Foundation (grant No. 448/09). The first author was also supported by the Chateaubriand scientific post-doctorate fellowships, Ministry of Science, French Government, 2007–2008. The second author was also supported in part by the Israel Science Foundation (grant No. 1178/06).
Funding
The research of the authors is supported by the Israel Science Foundation (grant No. 448/09). The first author was also supported by the Chateaubriand scientific post-doctorate fellowships, Ministry of Science, French Government, 2007–2008. The second author was also supported in part by the Israel Science Foundation (grant No. 1178/06).
| Funders | Funder number |
|---|---|
| Ministry of Science, French Government | 1178/06 |
| Israel Science Foundation | 448/09 |
Keywords
- Newton and lattice polytopes
- Tropical geometry
- max-plus algebra
- polyhedral complexes
- symmetry and symmetry