LisMath Seminar 

22/11/2017, 17:00 — 18:00 — Room 6.2.33, Faculty of Sciences of the Universidade de Lisboa
Carlos Sotillo, Universidade de Lisboa

Which parametrized surfaces are Quasi-Ordinary?

A germ of a singular surface $S$ is QO if there is a finite projection $p:S\to \mathbb C^2$ such that its discriminant is normal crossings. A QO surface admits a very special parametrization, that is a natural generalization of the Puiseux parametrization of a plane curve. The purpose of this seminar is to find criteria to determine if a surface $S$ with a parametrization $(u,v) \mapsto (x(u,v),y(u,v),z(u,v))$ is QO. For instance, if the semigroup of the surface $S$ is the semigroup of a QO surface, is the surface $S$ QO?

Bibliography:

[1] Gonzalez Perez, The semigroup of a quasi-ordinary hypersurface, http://www.mat.ucm.es/~pdperezg/semi4

[2] Gonzalez Perez, Quasi-ordinary Singularities via toric Geometry, http://www.mat.ucm.es/~pdperezg/PhD-Es-gonzalez.pdf

[3] Patrick Popescu-Pampu, On the analytic invariance of the semigroup of a QO hyperface singularity, http://math.univ-lille1.fr/~popescu/04-Duke.pdf

See also

sotillo.pdf