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Full-Text Articles in Physical Sciences and Mathematics
A Tropical Approach To The Brill-Noether Theory Over Hurwitz Spaces, Kaelin Cook-Powell
A Tropical Approach To The Brill-Noether Theory Over Hurwitz Spaces, Kaelin Cook-Powell
Theses and Dissertations--Mathematics
The geometry of a curve can be analyzed in many ways. One way of doing this is to study the set of all divisors on a curve of prescribed rank and degree, known as a Brill-Noether variety. A sequence of results, starting in the 1980s, answered several fundamental questions about these varieties for general curves. However, many of these questions are still unanswered if we restrict to special families of curves. This dissertation has three main goals. First, we examine Brill-Noether varieties for these special families and provide combinatorial descriptions of their irreducible components. Second, we provide a natural generalization …
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 definitions 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.
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
Theses and Dissertations
This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.