The Library
Tropical ideals
Tools
Maclagan, Diane and Rincón, Felipe (2018) Tropical ideals. Compositio Mathematica, 154 (3). pp. 640-670. doi:10.1112/S0010437X17008004 ISSN 0010-437X.
|
PDF
WRAP-Tropical-ideals-Maclagan-2017.pdf - Accepted Version - Requires a PDF viewer. Download (975Kb) | Preview |
Official URL: https://doi.org/10.1112/S0010437X17008004
Abstract
We introduce and study a special class of ideals, called tropical ideals, in the semiring of tropical polynomials, with the goal of developing a useful and solid algebraic foundation for tropical geometry. The class of tropical ideals strictly includes the tropicalizations of classical ideals, and allows us to define subschemes of tropical toric varieties, generalizing Giansiracusa and Giansiracusa [Equations of tropical varieties, Duke Math. J. 165 (2016), 3379–3433]. We investigate some of the basic structure of tropical ideals, and show that they satisfy many desirable properties that mimic the classical setup. In particular, every tropical ideal has an associated variety, which we prove is always a finite polyhedral complex. In addition we show that tropical ideals satisfy the ascending chain condition, even though they are typically not finitely generated, and also the weak Nullstellensatz.
Item Type: | Journal Article | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Tropical geometry, Polynomials | ||||||||||||
Journal or Publication Title: | Compositio Mathematica | ||||||||||||
Publisher: | Cambridge University Press | ||||||||||||
ISSN: | 0010-437X | ||||||||||||
Official Date: | March 2018 | ||||||||||||
Dates: |
|
||||||||||||
Volume: | 154 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 640-670 | ||||||||||||
DOI: | 10.1112/S0010437X17008004 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 11 December 2017 | ||||||||||||
Date of first compliant Open Access: | 2 May 2018 | ||||||||||||
RIOXX Funder/Project Grant: |
|
||||||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year