Researcher ORCID Identifier
0000-0003-4185-0311
Graduation Year
2021
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Dagan Karp
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2021 Natasha Zetta Crepeau
Abstract
Tropical geometry uses the minimum and addition operations to consider tropical versions of the curves, surfaces, and more generally the zero set of polynomials, called varieties, that are the objects of study in classical algebraic geometry. One known result in classical geometry is that smooth quadric surfaces in three-dimensional projective space, $\mathbb{P}^3$, are doubly ruled, and those rulings form a disjoint union of conics in $\mathbb{P}^5$. We wish to see if the same result holds for smooth tropical quadrics. We use the Fundamental Theorem of Tropical Algebraic Geometry to outline an approach to studying how lines lift onto a tropical quadric, which is necessary for understanding what lines are on smooth tropical quadrics and their structure. We also provide suggestions of how computational tools can be used to implement the approach.
Recommended Citation
Crepeau, Natasha, "On the Tropicalization of Lines onto Tropical Quadrics" (2021). HMC Senior Theses. 248.
https://scholarship.claremont.edu/hmc_theses/248
