Tropical enumerative invariants of ๐ฝ0 and ๐ฝ2
Marina Franz, Hannah Markwig ยท Advances in Geometry ยท 2010
Abstract There is an equation relating numbers of curves on satisfying incidence conditions and numbers of curves on ๐ฝ2 satisfying incidence conditions. The purpose of this paper is to give a tropical proof of this equation in the case of rational curves. We use induction on the degree and two Kontsevich-type formulas for curves on ๐ฝ0 and on ๐ฝ2. The formula for ๐ฝ2 was not known before and is proved using tropical geometry.