The enumerative geometry of rational and elliptic tropical curves and a Riemann-Roch theorem in tropical geometry

  • This thesis is devoted to the study of tropical curves with emphasis on their enumerative geometry. Major results include a conceptual proof of the fact that the number of rational tropical plane curves interpolating an appropriate number of general points is independent of the choice of points, the computation of intersection products of Psi-classes on the moduli space of rational tropical curves, a computation of the number of tropical elliptic plane curves of given degree and fixed tropical j-invariant as well as a tropical analogue of the Riemann-Roch theorem for algebraic curves. The result are obtained in joint work with Hannah Markwig and/or Andreas Gathmann.
  • Die enumerative Geometrie rationaler und elliptischer tropischer Kurven und ein Riemann-Roch Satz in der tropischen Geometrie

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Author:Michael Kerber
Advisor:Andreas Gathmann
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2008
Year of Publication:2008
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2008/12/12
Date of the Publication (Server):2009/08/28
GND-Keyword:Tropische Geometrie
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011