Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
The Tropical Jacobian Of A Tropical Elliptic Curve Is S^1(Q), Darryl Gene Wade
The Tropical Jacobian Of A Tropical Elliptic Curve Is S^1(Q), Darryl Gene Wade
Theses and Dissertations
We establish consistent deļ¬nitions for divisors, principal divisors, and Jacobians of a tropical elliptic curve and show that for a tropical elliptic cubic C , the associated Jacobian (or zero divisor class group) is the group S^1(Q).
Complete Tropical Bezout's Theorem And Intersection Theory In The Tropical Projective Plane, Gretchen Rimmasch
Complete Tropical Bezout's Theorem And Intersection Theory In The Tropical Projective Plane, Gretchen Rimmasch
Theses and Dissertations
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.