On regularity conditions at infinity

Journal of Singularities
volume 10 (2014), 54-66

Received 8 January 2013. Received in revised form 31 July 2013.

DOI: 10.5427/jsing.2014.10c

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Abstract:

Let f: X -> K^p be a restriction of a polynomial mapping on X, where X is a smooth affine variety contained in K^n. We prove the equivalence of regularity conditions at infinity, which are useful to control the bifurcation set of f.

Keywords:

polynomial mapping, bifurcation values, Rabier condition, $t$-regularity, non-properness set, fibration, regularity at infinity

Mathematical Subject Classification:

14D06, 51N10, 32S20

Author(s) information:

L. R. G. Dias
Faculdade de Matemática
Universidade Federal de Uberlândia
Av. João Naves de Ávila, 2121
1F153 - CEP: 38.408-100, Uberlândia, Brazil
email: lrgdias@famat.ufu.br