Betti Bounds of Polynomials

Dirk Siersma (1) , Mihai Tibar (2)

1 Institute of Mathematics
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Dirk Siersma, Mihai Tibar. Betti Bounds of Polynomials. Moscow Math. J., 2011, 11 (3), pp.599-615. ⟨hal-00568151⟩