On Intersections of Algebraic Curves and Applications to Elliptic Curves

University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

Author: Karl Lindén; [2018]

Keywords: Bezout s theorem; Max Noether s fundamental theorem; Pappus s theorem; Pascal s theorem; Chasles theorem; algebraic curves; elliptic curves; Mathematics and Statistics;

Abstract: In this thesis we state and give elementary proofs for some fundamental results about intersections of algebraic curves, namely Bezout's, Max Noether's, Pappus's, Pascal's and Chasles' theorems. Our main tools are linear algebra and basic ring theory. We conclude the thesis by applying the results to elliptic curves.

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