Complex Projective Cubic Plane Curves

Abstract

This report aims to classify the study of all irreducible cubic curves in $\mathbb{C}\mathbb{P}^2$ (complex projective 2-space). To do so, it builds up the necessary foundational ideas about algebraic plane curves needed to prove two primary theorems in order: Bézout's Theorem, followed by the Cayley-Bacharach Theorem. Using these two significant results, it will finally move towards classification, with a specific emphasis on the study of elliptic curves through an algebraic and topological lens.

Bibliography

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