Tropical schemes, tropical cycles, and valuated matroids

DOI10.4171/JEMS/932MaRDI QIDQ2302847

Felipe Rincón, Diane MacLagan

Publication date: 26 February 2020

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4654

zbMATH Keywords

valuated matroidtropical scheme

Mathematics Subject Classification ID

Combinatorial aspects of tropical varieties (14T15) Geometric aspects of tropical varieties (14T20) Combinatorial aspects of matroids and geometric lattices (05B35) Foundations of tropical geometry and relations with algebra (14T10)

Related Items

Congruences and coordinate semirings of tropical varieties, The moduli space of matroids, A unifying approach to tropicalization, Tropical geometry over the tropical hyperfield, Paving tropical ideals, Dynamical tropicalisation, A general framework for tropical differential equations, Higher balancing for tropical manifolds, A MODULI STACK OF TROPICAL CURVES, The topological shadow of \(\mathbb{F}_1\)-geometry: congruence spaces, Tropical methods in geometry. Abstracts from the workshop held May 14--19, 2023, Categories with negation, Tropical ideals, A module-theoretic approach to matroids, Picard groups for tropical toric schemes, Varieties of tropical ideals are balanced, The universal tropicalization and the Berkovich analytification

Uses Software

• Binomials.m2
• TropLi

Cites Work

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• Local tropical linear spaces
• Decompositions of commutative monoid congruences and binomial ideals.
• Equations of tropical varieties
• Isotropical linear spaces and valuated Delta-matroids
• Valuated matroids
• Matroid valuation on independent sets
• Subdominant matroid ultrametrics
• Gérard-Levelt membranes
• Realization Spaces for Tropical Fans
• On circuit valuation of matroids