Dirk Siersma – Betti Bounds of Polynomials

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Date(s) - 19 janvier 2012

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We will talk about the topological properties of polynomial functions $f : C^n \to C$. We will give a short overview of known results about the fibres of these mappings and the effect of critical points. Next we focus on polynomials of degree $d$ having the top Betti number of the general fibre close to the maximum. They have a rather simple description. First there is 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