Intersecting $\psi$classes on $M_{0,w}^{\mathrm{trop}}$
Abstract
In this paper, we study the intersection products of weighted tropical $\psi$classes, in arbitrary dimensions, on the moduli space of tropical weighted stable curves. We introduce the tropical GromovWitten multiplicity at each vertex of a given tropical curve. This concept enables us to prove that the weight of a maximal cone in an intersection of $\psi$classes decomposes as the product of tropical GromovWitten multiplicities at all vertices of the cone's associated tropical curves. Along the way, we define weighted tropical $\psi$classes on these moduli spaces, furnish a combinatorial characterisation thereof and realise them as multiples of tropical Weil divisors of a family of rational functions on these moduli spaces. In the special case of topdimensional intersections, our result confirms the correspondence between the tropical GromovWitten invariants and their algebrogeometric counterparts explicitly on these weighted moduli spaces.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.00875
 Bibcode:
 2021arXiv210800875A
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Geometry;
 05E14 05E14 05E14;
 14N35;
 14T15
 EPrint:
 25 pages