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.