Abstract
In this paper, we consider weighted counts of tropical plane curves of particular combinatorial type through a certain number of generic points. We give a criterion, effectively balancing, derived from tropical intersection theory on the secondary fan, for a weighted count to give a number invariant of the position of the points. By computing a certain intersection multiplicity, we determine which weighted counts in our approach replicates Mikhalkin's computation of Gromov–Witten invariants although we do not know if such a count is effectively balanced. This begins to address a question raised by Dickenstein, Feichtner, and Sturmfels. We also give a geometric interpretation of the numbers we produce involving Chow quotients, and provide a counterexample showing that the tropical Severi variety is not always supported on the secondary fan.
© de Gruyter 2009
