Tropical rational curves with first order tangency via WDVV

Abstract

In this article, we study the tropical counterpart of the enumeration of rational curves in ${\mathbb{CP}}^2$ with first order tangency. We use the tropical analogue of the WDVV technique to compute rational tropical plane curves of degree $d$ tangent to a degree $l$ tropical plane curve and passing through $3d-2$ points in general position. As Mikhalkin's correspondence suggests, our numbers agree with earlier results on tangency in complex geometry.

arXiv comment14 pages, 5 figures