“Simion Stoilow” Institute of Mathematics
of the Romanian Academy
“Betti bounds of polynomials”
Mihai Tibar (Université Lille 1)
ABSTRACT:
We initiate a classification of polynomials
$f : \bC^n \to \bC$ of degree $d$ having
the top Betti number of the general fibre close to the maximum.
We find a range in which the polynomial must have isolated
singularities and
another range where it may have at most a line singularity of Morse
transversal type, besides controlled singularities at infinity. Our
method uses deformations into particular pencils with non-isolated
singularities.