منابع مشابه
The Realizability of Curves in a Tropical Plane
Let E be a plane in an algebraic torus over an algebraically closed field. Given a balanced 1-dimensional fan C in the tropicalization of E, i. e. in the Bergman fan of the corresponding matroid, we give a complete algorithmic answer to the question whether or not C can be realized as the tropicalization of an algebraic curve contained in E. Moreover, in the case of realizability the algorithm ...
متن کاملTropical Curves
A tropical curve is a graph with specified edge lengths, some of which may be infinite. Various facts and attributes about algebraic curves have analogs for tropical curves. In this article, we focus on divisors and linear series, and prove the Riemann-Roch formula for divisors on tropical curves. We describe two ways in which algebraic curves may be transformed into tropical curves: by aboemas...
متن کاملDuality of Tropical Curves
Duality of curves is an important aspect of the “classical” algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using the development of an algebraic “mechanism”, based on “distortion” values, geometric and convexity properties are analyzed. Specifically, we discuss some significant aspe...
متن کاملTropical complete intersection curves
A tropical complete intersection curve C ⊆ Rn+1 is a transversal intersection of n smooth tropical hypersurfaces. We give a formula for the number of vertices of C given by the degrees of the tropical hypersurfaces. We also compute the genus of C (defined as the number of independent cycles of C) when C is smooth and connected. 1 Notation and definitions We work over the tropical semifield Rtr=...
متن کاملKnots and Tropical Curves
A sequence of rational functions in a variable q is q-holonomic if it satisfies a linear recursion with coefficients polynomials in q and qn. In the paper, we assign a tropical curve to every q-holonomic sequence, which is closely related to the degree of the sequence with respect to q. In particular, we assign a tropical curve to every knot which is determined by the Jones polynomial of the kn...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2015
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnv269