Genus 0 logarithmic and tropical fixed‐domain counts for Hirzebruch surfaces

Abstract For a non‐singular projective toric variety , the virtual logarithmic Tevelev degrees are defined as the virtual degree of the morphism from the moduli stack of logarithmic stable maps to the product . In this paper, after proving that Mikhalkin's correspondence theorem holds in genus 0 for logarithmic virtual Tevelev degrees, we use tropical methods to provide closed formulas for the case in which is a Hirzebruch surface. In order to do so, we explicitly list all the tropical curves contributing to the count.