THREE TROPICAL ENUMERATIVE PROBLEMS

Abstract. In this survey, we describe three tropical enumerative prob-lems and the corresponding moduli spaces of tropical curves. They have the structure of weighted polyhedral complexes. We observe similarities in the definitions of the weights, aiming at a better understanding of the tropical structure of the moduli spaces. 1. introduction In tropical geometry, algebraic varieties are degenerated to certain piece-wise linear objects called tropical varieties. This process loses a lot of information, but many properties of the algebraic variety can be read off the tropical variety, and many theorems that hold for the algebraic side remarkably continue to hold on the tropical side. Since tropical varieties are piece-wise linear, they are in principle easier to understand than algebraic varieties and combinatorial methods apply. Thus there is hope that we can use tropical geometry to derive theorems in algebraic geometry. One of the fields in which tropical geometry has had significant succes