ISBN 9783843916691

978-3-8439-1669-1, Reihe Mathematik

Carolin Torchiani
Enumerative geometry of rational and elliptic tropical curves in R m

143 Seiten, Dissertation Technische Universität Kaiserslautern (2014), Softcover, A4

Zusammenfassung / Abstract

We study enumerative tropical questions in a real coordinate space of m dimension using tropical intersection theory. First, we establish a recursive formula that allows us to determine the number of rational tropical curves of degree d in m-space. This number coincides with its algebraic counterpart. Furthermore, we develop a combinatorial notion of a well-spaced elliptic tropical curve in m-space, which is based on the known necessary and sufficient conditions for the realizability of elliptic tropical curves. Finally, we prove that the number of well-spaced elliptic tropical curves passing a general configuration of translated tropical fans in m-space, counted with an intersection-theoretic multiplicity, does not depend on the position of the translated fans.