منابع مشابه
Krull - Tropical Hypersurfaces
The concepts of tropical semiring and tropical hypersurface, are extended to the case of an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator “tropicalization” we conclude with an extension of Kapranov’s theorem to algebraically closed fields together with a valuation over...
متن کاملSingular Tropical Hypersurfaces
We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal intersection points of planar tropical curves.
متن کاملComplex Tropical Localization, Coamoebas, and Mirror Tropical Hypersurfaces
We introduce in this paper the concept of tropical mirror hypersurfaces and we prove a complex tropical localization Theorem which is a version of Kapranov's Theorem [K-00] in tropical geometry. We give a geometric and a topological equivalence between coamoebas of complex algebraic hypersurfaces de ned by a maximally sparse polynomial and coamoebas of maximally sparse complex tropical hypersur...
متن کاملIntersection multiplicity numbers between tropical hypersurfaces
We present several formulas for the intersection multiplicity numbers considered in [3]. These numbers are associated to any dimensional cell of the common intersection of the tropical hypersurfaces. The first formula involves a sum of generalized mixed volumes, and turns out to be equal to the absolute value of the Euler characteristic of some complex toric complete intersection. Another formu...
متن کاملObstructions to Lifting Tropical Curves in Hypersurfaces
Tropicalization takes a curve in a hypersurface in 3-space to a balanced rational weighted graph in a tropical surface. In this paper, we study the ‘lifting’ problem: given a graph in a tropical surface, can one find a corresponding algebraic curve in a hypersurface? We develop specific combinatorial obstructions to a graph lifting by studying the factorizations of polynomials with particular N...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2010
ISSN: 0240-2963
DOI: 10.5802/afst.1255