2011/01/19 by Dirk Siersma, Mihai Tibar
Mathematics · #math.AG #math.CV #msc:32S30 #msc:58K60 #msc:55R55 #msc:32S50
published as Moscow Math. J. 11, no. 3 (2011), 599-615 · 17 pages, 2 figures
arxiv created 2011/01/19 · arxiv updated 2011/09/01
We initiate a classification of complex polynomials f 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.