Thom irregularity and Milnor tube fibrations
We find natural and convenient conditions which allow us to produce classes of genuine real map germs with Milnor tube fibration, either with Thom regularity or without it.
math.AG↗
arXiv subjects
M. Tibar
Publications and source records attributed to M. Tibar.
On the geometry of regular maps from a quasi-projective surface to a curve
By exploring the consequences of the triviality of the monodromy group for a class of surfaces of which the mixed Hodge structure is pure, we extend results of Miyanishi and Sugie, Dimca, Zaidenberg and Kaliman.
math.AG↗
On Newton non-degeneracy of polynomial mappings
We introduce a new non-degeneracy condition at infinity for a real or a mixed polynomial mapping $F$ which allows us to approximate its bifurcation locus in terms of certain Newton polyhedra. We derive a sufficiency result for the Jacobian problem in the setting of mixed mappings.
math.AG↗
Regularity at infinity of real mappings and a Morse-Sard theorem
We prove a new Morse-Sard type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for $C^2$ mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the $t$-regularity and its bridge toward the $ρ$-regularity which implies topological triviality at infinity.
math.AG↗
Contact boundaries of hypersurface singularities and of complex polynomials
We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
math.CV↗