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Classification at Infinity of Polynomials of Degree 3 in 3 Variables by Ribeiro, Nilva Rodrigues is a scholarly article available to read on EtoBox.

What is Classification at Infinity of Polynomials of Degree 3 in 3 Variables about?

We classify singularities at infinity of polynomials of degree 3 in 3 variables, $ 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 Milnor number of an isolated singularity at infinity, when we pass from the special fiber to a generic fiber. As an application of the results, we investigate the existence of global fibrations of degree 3 polynomials in $\mathbb{C}^3$ and search for information about the topology of the fibers in each equivalence class.

Author

Ribeiro, Nilva Rodrigues

Published

2022

Language

EN