Abstract
We initiate a classification of polynomials f : Cn - C 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 one line singularity of Morse transversal type. Our method uses deformations into
particular pencils with non-isolated singularities
| Original language | English |
|---|---|
| Pages (from-to) | 599-615 |
| Number of pages | 17 |
| Journal | Moscow Mathematical Journal |
| Volume | 11 |
| Issue number | 3 |
| Publication status | Published - 2011 |
Keywords
- Deformation of hypersurfaces and polynomials
- Betti numbers
- classification
- general fibres
- singularities at infinity
- boundary singularities