Obstructions to Lifting Tropical Curves in Hypersurfaces
نویسنده
چکیده
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 Newton polygons. We also give examples to show which lifting questions are purely combinatorial.
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