Intersection numbers on tropical Hassett spaces

TL;DR

This paper investigates intersection theory on tropical Hassett spaces, generalizing previous results, and finds that tropical intersection products match classical ones in top dimension, with nonnegative weights linked to tropical curve combinatorics.

Contribution

It extends intersection computations to tropical Hassett spaces, providing a combinatorial interpretation and showing the tropical and classical intersection products coincide in top dimension.

Findings

Weights of maximal cones are nonnegative and combinatorially interpretable.

Tropical intersection products in top dimension match classical intersection products.

Abstract

We study the intersection of tropical psi-classes on tropical heavy/light Hassett spaces, generalising a result of Kerber--Markwig for tropical moduli spaces of rational stable curves with distinct marked points. Our computation reveals that the weight of a maximal cone in an intersection has a combinatorial intepretation in terms of the underlying tropical curve and it is always nonnegative. In particular, our result specialises to that, in top dimension, the tropical intersection product coincides with its classical counterpart.