Generic Tropical Varieties

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Titel: Generic Tropical Varieties
Autor(en): Schmitz, Kirsten
Erstgutachter: Prof. Dr. Tim Roemer
Zweitgutachter: Prof. Dr. Hannah Markwig
Zusammenfassung: The field of algebraic tropical geometry establishes a deep connection between algebraic geometry and combinatorics by associating to certain classical algebraic varieties so called tropical varieties, which are polyhedral complexes in some real vectorspaces. Tropical varieties are closely related to the Groebner complexes of the ideal defining the classical variety. In this thesis the tropical variety of an ideal is studied under a generic change of coodinates. Analogously to the existence of generic initial ideals the existence of generic Groebner complexes and generic tropical varieties is proved. Moreover, it is shown that in the constant coefficient case information on the invariants dimension, Hilbert-Samuel multiplicity and depth of the corresponding coordinate rings can be obtained from generic tropical varieties.
URL: https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201104278080
Schlagworte: Tropical Geometry; Groebner Fan; Generic Initial Ideal; Polyhedral Complex
Erscheinungsdatum: 27-Apr-2011
Publikationstyp: Dissertation oder Habilitation [doctoralThesis]
Enthalten in den Sammlungen:FB06 - E-Dissertationen

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