Classification at infinity of polynomials of degree 3 in 3 variables

Journal of Singularities
volume 25 (2022), 377-392

Received: 31 January 2021. Received in revised form: 8 July 2022.

DOI: 10.5427/jsing.2022.25r

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Abstract:

We classify singularities at infinity of polynomials of degree 3 in 3 variables. 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 complex affine 3-space and search for information about the topology of the fibers in each equivalence class.

Author(s) information:

Nilva Rodrigues Ribeiro
Universidade Federal de Viçosa-Campus
Rio Paranaíba
Instituto de Ciências Exatas e Tecnológicas
Rodovia MG-230, Km 7 Rio Paranaíba/MG
CEP: 38810-000 Caixa Postal 22, Brazil
nilvaufv@gmail.com