(University of Oregon, 2023-05) Richter, Karl; Addinton, Nicolas; Brooke, Corey
This thesis is primarily concerned with the fact that the general quartic surface does not contain a line or a conic section. More formally, the set of quartic surfaces containing lines or conic sections has measure zero.
This result follows from an important result in algebraic geometry, the Noether-Lefschetz theo-rem; however, this paper will use elemenary techniques in algebra and analysis to come to the same conclusion. In addition, this paper will introduce the idea of curves, surfaces, and their parameter spaces.
