… , Figure 1.8 depicts a smooth cubic curve in R2 before the … of tropical geometry with tropical
hypersurfaces in Rn. Recall from the introduction that R can be regarded as the set of tropical …

… of tropical geometry, and we show by way of elementary examples how tropical methods can
… We now focus on tropical curves whose Newton polygons are the standard triangles with …

… Superabundant curves cause a great deal of difficulty for tropical geometry, and we shall
handle this by restricting further to plane curves, ie, dimM R = 2. Furthermore, as we shall only …

… We start the exposition with tropical curves in the plane and their applications to problems
in classical enumerative geometry, and continue with a look at more general tropical varieties …

… relations to classical geometry via the notion of amoebas of algebraic curves in Section 3 …
For example, starting with the tropical curve depicted in Figure 7a, we obtain the curve …

… In Chapter 5, we turn to the study of the tropicalizations of curves. This field was … of tropical
thinking. We take a very different approach than Mikhalkin and, rather than study curves via …

… This led to the definition of an abstract tropical curve as a … of tropical geometry involved
finding tropical analogues of theorems about algebraic curves and their enumerative geometry. …

… to cover all facets of tropical geometry. For instance, we … tropical geometry considered in
the next two chapters we just refer the reader to [42], [43], [44]. To relate abstract tropical curves …

… the fact that tropical geometry is a limit of classical geometry. If … : Tropical geometry is the
image of classical geometry under … First, we should note that tropical curves first appeared under …

… in terms of tropical elliptic curves with fixed tropical j-invariant satisfying linear constraints.
Our theorems generalize previously published correspondence theorems in tropical geometry, …