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We classify singularities at infinity of polynomials of degree 3 in 3variables, $ f (x_0, x_1, x_2) = f_1 (x_0, x_1, x_2) + f_2 (x_0, x_1, x_2) +f_3 (x_0, x_1, x_2) $, $ f_i $ homogeneous polynomial of degree $ i $, $ i =1,2,3 $. Based on this classification, we calculate the jump in the Milnornumber of an isolated singularity at infinity, when we pass from the specialfiber to a generic fiber. As an application of the results, we investigate theexistence of global fibrations of degree 3 polynomials in $\mathbb{C}^3$ andsearch for information about the topology of the fibers in each equivalenceclass.

Classification at infinity of polynomials of degree 3 in 3 variables