Tropical refined curve counting from higher genera and lambda classes

Abstract

Block and Göttsche have defined a q-number refinement of counts of tropical curves in R2. Under the change of variables q= eiu, we show that the result is a generating series of higher genus log Gromov–Witten invariants with insertion of a lambda class. This gives a geometric interpretation of the Block-Göttsche invariants and makes their deformation invariance manifest.