Seminar of algebraic geometry - Josef Schicho (29.11.2018)

Thursday 29.11.2018 at 10:00, Lecture room M/216

21. 11. 2018 21.40 hod.
By: Jana Chalmovianska

A.Univ.-Prof. Dr. Josef Schicho (RISC, JKU Linz, Rakúsko):
Recognizing an Algebraic Surface from its 2D Projection

Abstract:
An algebraic surface is given by its equation, the zero set of a polynomial in four homogeneous variables. Its picture under central projection is computed as the zero set of its discriminant: a plane algebraic curve. Can we recover the equation of an algebraic surface by its discriminant?

If the surface is nonsingular, then the answer is yes, by a result of d'Almeida. If we allow also "generic" singularities, then the there is sometimes a finite list of possibilities. This talk explains the reconstruction method and discusses the ambiguities in the singular case.