Daet and Time: Wednesday, 4th Nov 2020 at 7 pm
Speaker:Parvez Rasul
Title: Bezout’s theorem for algebraic curves in plane
Abstract: Algebraic geometry is concerned with the study of the properties of certain geometric objects (which are mainly solution sets of systems of polynomial equations) using abstract algebra. One of the earliest results to this end is Bézout’s theorem, which relates the number of points at which two polynomial curves intersect to the degrees of the generating polynomials. Here we reproduce an elementary proof of Bézout’s theorem for algebraic curves in plane. It states that if we have two algebraic plane curves, defined over an algebraically closed field and given by zero sets of polynomials of degrees n and m, then the number of points where these curves intersect is exactly nm if we count ”multiple intersections” and ”intersections at infinity”. To formulate and prove the theorem rigorously we go through some concepts which lie at the heart of algebraic geometry like projective space and intersection multiplicities at a common point of two curves.
Google Meet Link:
https://meet.google.com/hhk-ijhb-ivr