Structural Results on Generic Tropical Varieties

From CRCG-Wiki

We briefly review the definition and existence result of generic tropical varieties of graded ideals in the constant coefficient case. Natural questions are now, what a generic tropical variety can look like and which algebraic invariants of the ideal can be recovered from it. We describe the generic tropical variety as a set and see that this only depends on the dimension of the ideal. Its fan structure, however, contains more information and we will give some structural results on these fans.