Abstract

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.

Degree

PhD

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2008-07-11

Document Type

Dissertation

Handle

http://hdl.lib.byu.edu/1877/etd2507

Keywords

tropical Bezout, tropical, tropical intersection theory, tropical resultant

Included in

Mathematics Commons

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