Obstructions to lifting tropical curves in hypersurfaces
Tristram Bogart, Eric Katz · arXiv (Cornell University) · 2010
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.