An Introduction to Algebraic Geometry: Polygons, Parameterizations, and Equations

Abstract

We explain how four surfaces that are ubiquitous in algebraic geometry may be obtained from convex polygons whose vertices have integer coordinates, realizing these surfaces as examples of toric varieties. We highlight the combinatorial and algebraic properties revealed by this construction. Our claim of novelty is in our particular combination of the toric, classical geometric, and algebraic points of view.