The diagonal of tropical matroid varieties and cycle intersections

Abstract

We define an intersection product of tropical cycles on matroid varieties (via cutting out the diagonal) and show that it is well-behaved. In particular, this enables us to intersect cycles on moduli spaces of tropical rational marked curves $M_{0,n}$ and $M_{0,n}({\mathbb{R}}^r,d)$. This intersection product can be extended to smooth varieties (whose local models are matroid varieties). We also study pull-backs of cycles and rational equivalence.

23 pages, 5 figures

References in corpus (1)

• Matroid polytopes, nested sets and Bergman fans

Cited by in corpus (22)

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• Computing Tropical Linear Spaces
• Lefschetz (1,1)-theorem in tropical geometry
• Chern-Schwartz-MacPherson cycles of matroids
• Intersection Theory on Tropicalizations of Toroidal Embeddings
• Lifting representations of finite reductive groups I: Semisimple conjugacy classes
• A-Tint: A polymake extension for algorithmic tropical intersection theory
• The intersection ring of matroids
• Correspondence Theorems via Tropicalizations of Moduli Spaces
• Local tropical linear spaces
• Perfect matroids over hyperfields
• Universal families of rational tropical curves
• Real phase structures on matroid fans and matroid orientations
• Tautological cycles on tropical Jacobians
• Intersection Theory on Linear Subvarieties of Toric Varieties
• Intersection numbers on tropical Hassett spaces
• The tropical Poincaré-Hopf theorem
• Cocycles on tropical varieties via piecewise polynomials
• Tropical $\psi$ classes
• Combinatorics of tropical Hurwitz cycles
• Tropical Moduli Space of Rational Graphically Stable Curves
• Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical cycles