Generic Tropical Varieties

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Title: Generic Tropical Varieties
Authors: Schmitz, Kirsten
Thesis advisor: Prof. Dr. Tim Roemer
Thesis referee: Prof. Dr. Hannah Markwig
Abstract: 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.
Subject Keywords: Tropical Geometry; Groebner Fan; Generic Initial Ideal; Polyhedral Complex
Issue Date: 27-Apr-2011
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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