In this dissertation we prove a version of the tropical Bezout's theorem which is applicable to all tropical projective plane curves. There is a version of tropical Bezout's theorem presented in other works which applies in special cases, but we provide a proof of the theorem for all tropical projective plane curves. We provide several different definitions of intersection multiplicity and show that they all agree. Finally, we will use a tropical resultant to determine the intersection multiplicity of points of intersection at infinite distance. Using these new definitions of intersection multiplicity we prove the complete tropical Bezout's theorem.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Rimmasch, Gretchen, "Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane" (2008). Theses and Dissertations. 1505.
tropical Bezout, tropical, tropical intersection theory, tropical resultant