Graduation Year
2013
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Dagan Karp
Reader 2
Angelica Cueto
Terms of Use & License Information
Rights Information
© 2013 Kevin O'Neill
Abstract
Classical algebraic geometry is the study of curves, surfaces, and other varieties defined as the zero set of polynomial equations. Tropical geometry is a branch of algebraic geometry based on the tropical semiring with operations minimization and addition. We introduce the notions of projective space and tropical projective space, which are well-suited for answering enumerative questions, like ours. We attempt to describe the set of tropical lines contained in a tropical quadric surface in $\mathbb{TP}^3$. Analogies with the classical problem and computational techniques based on the idea of a tropical parameterization suggest that the answer is the union of two disjoint conics in $\mathbb{TP}^5$.
Recommended Citation
O'Neill, Kevin, "Lines in Tropical Quadrics" (2013). HMC Senior Theses. 43.
https://scholarship.claremont.edu/hmc_theses/43
