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
Author: | Michael Kerber |
---|---|
URN: | urn:nbn:de:hbz:386-kluedo-23170 |
Advisor: | Andreas Gathmann |
Document Type: | Doctoral Thesis |
Language of publication: | English |
Year of Completion: | 2008 |
Year of first Publication: | 2008 |
Publishing Institution: | Technische Universität Kaiserslautern |
Granting Institution: | 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 |