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Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane

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.

Identiferoai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-2504
Date11 July 2008
CreatorsRimmasch, Gretchen
PublisherBYU ScholarsArchive
Source SetsBrigham Young University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations
Rightshttp://lib.byu.edu/about/copyright/

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