Tropical linear systems and the realizability problem
Matthew Dupraz
TL;DR
This thesis investigates the geometry of tropical curves, establishing bounds on tropical submodules and characterizing realizable canonical divisors to connect tropical and algebraic geometry.
Contribution
It introduces a lower bound on tropical submodule dimensions and characterizes realizable canonical divisors, advancing the understanding of tropical geometry's algebraic connections.
Findings
Established a lower bound on tropical submodule dimensions based on Baker-Norine rank
Provided a characterization of realizable canonical divisors
Connected tropical geometry concepts to algebraic geometry
Abstract
This thesis delves into the geometry of abstract tropical curves, exploring their complete linear system and associated tropical submodules. We establish a lower bound on the dimension of tropical submodules in terms of the Baker-Norine rank. Furthermore, the work provides a characterization of realizable canonical divisors, addressing a fundamental problem in connecting tropical geometry to its algebraic counterpart.
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Taxonomy
TopicsPolynomial and algebraic computation · Formal Methods in Verification · Advanced Differential Equations and Dynamical Systems