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Kevin O'Neill

Picture of Kevin O'Neill.

Thesis

Lines in Tropical Quadrics

Advisor
Dagan Karp
Second Reader(s)
Angelica Cueto

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

Proposal

Tropical Fano Schemes in TP^3

Additional Materials

Poster