10 oct 2017 -- 13:00
Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
How many surfaces of a given degree present singularities of some specified type and pass through an appropriate number of points? We focus on counting singular surfaces with certain non isolated singularities: e.g., Whitney's umbrella, quartics singular along atwisted cubic, etc. We give a proof for the polynomial nature of the formulae and make it explicit in a few cases. Conjecturally the degree of the formula is twice the dimension of the family of curves imposed in the singular locus. We manage to bound it by thrice that dimension. We draw essentially from previous joint work with Angelo Lopez and Fernando Cukierman.