The diagonal of tropical matroid varieties and cycle intersections

By Georges François, Johannes Rau. 2010

56 citations recorded by the source corpus.

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 $$\mathcal M _n$$ and $$\mathcal M _n^{\text{ lab}}(\Delta , \mathbb R ^r)$$. 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/48790b821240ccfccd91ea662609789ac1bf3894

How researchers see this paper

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In Algebra and Number Theory

1. Dhruv Ranganathan
2. Simon Hampe
3. Hannah Markwig
4. Renzo Cavalieri
5. Martin Ulirsch

In Computational Theory and Mathematics

1. Dhruv Ranganathan
2. Renzo Cavalieri
3. Simon Hampe
4. Hannah Markwig
5. Martin Ulirsch
6. G. Mikhalkin

In Geometry and Topology

1. Dhruv Ranganathan
2. Renzo Cavalieri
3. Simon Hampe
4. Hannah Markwig
5. Martin Ulirsch
6. G. Mikhalkin

Citations in the corpus

• MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY (2014, methodology): “Applying the diagonal functions φ defined in [9] cuts out the diagonal ∆Rr0 with weight 1 on the right hand side.”