Alexandre Fernandes

Wednesday, September 9th, 2020. Gmeet at 4:20 pm

Title: Multiplicity of singular points

Abstract: The multiplicity of an algebraic curve C in the complex plane on a point p
of that curve is the number of points on the intersection of C with a general line
passing near p. One shows that p is a singular point of C if and only if this multiplicity
is bigger or equals 2. In this lecture, we show the classic concept of multiplicity of
singular points of complex algebraic sets (not necessarily complex curves) and we
approach the nature of the multiplicity of singular points as a geometrical invariant
under the perspective of the Multiplicity Conjecture (Zariski 1971) and results
obtained in joint works with L. Birbrair, J. de Bobadilla, J. E. Sampaio and M.
Verbtisky.