Tropical orbit spaces and moduli spaces of tropical curves [Elektronische Ressource] / Matthias Herold

FACHBEREICHMATHEMATIKKaiserslautern&Thesis INSTITUT DERECHERCHEpresented to receive the degree of Doktor der´MATHEMATIQUENaturwissenschaften (Doctor rerum naturalium,Dr.rer.nat) at Technische Universitat¨ Kaiserslautern, ´AVANCEEresp. Doctorat de Mathematiques´ at l’Universite´ deStrasbourg UMR 7501specialty MATHEMATICSStrasbourgMatthiasHeroldTropicalorbitspacesandmodulispacesoftropicalcurvesD 386Defended on January 25, 2011in front of the juryMr. A. Gathmann, supervisorMr. I. Itenberg, supervisorMr. J-J. Risler, reviewerMr. E. Shustin, reviewerwww.mathematik.uni-kl.deMr. A. Oancea, scientific memberwww-irma.u-strasbg.frMr. G. Pfister, scientificA main result of this thesis is a conceptual proof of the fact that the weighted number of tropicalcurves of given degree and genus, which pass through the right number of general points in the planer(resp., which pass through general points inR and represent a given point in the moduli space of genusg curves) is independent of the choices of points. Another main result is a new correspondence theorembetween plane tropical cycles and plane elliptic algebraic curves.Un principal résultat de la thèse est une preuve conceptionnelle du fait que le nombre pondéré decourbes tropicales de degré et genre donnés qui passent par le bon nombre de points en position générale2 rdansR (resp.