Betti bounds of polynomials
Publication date
2011
Authors
Siersma, Dirk
Tibar, M.
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Document Type
Article
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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
Keywords
Deformation of hypersurfaces and polynomials, Betti numbers, classification, general fibres, singularities at infinity, boundary singularities
Citation
Siersma, D & Tibar, M 2011, 'Betti bounds of polynomials', Moscow Mathematical Journal, vol. 11, no. 3, pp. 599-615. < http://www.mathjournals.org/mmj/vol11-3-2011/abst11-3-2011.html#siersma-tibar >