Lines and Conics in a Family of Quartic Surfaces
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Date
2023-05
Authors
Richter, Karl
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
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.
Description
42 pages
Keywords
Quartic Surfaces, Curves, Geometry, Algebra, Lines, Conics