Groebner fan içerisinde tropikal hiperyüzeyler.

Given an ideal I in the polynomial ring k[x1,… ,xn], the Groebner fan of I is a structure in R^n forming a polyhedral complex. Any ideal I has a tropicalization which is called the tropical variety associated to I. This variety is a piecewise linear object that is directly related to the Groebner fan of that ideal. The aim of this thesis is to have a better understanding of tropical varieties of codimension 1 and 2, and to observe that the tropical variety of a given ideal is in fact a sub-complex of the corresponding Groebner fan.