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.

Name thesis:degree_name

PhD

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Rimmasch, Gretchen

• tropical Bezout
• tropical
• tropical intersection theory
• tropical resultant
• Mathematics

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/1505

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-2504