“Simion Stoilow” Institute of Mathematics
of the Romanian Academy

“Betti bounds of polynomials”
Mihai Tibar (Université Lille 1)


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.