Obstructions to Lifting Tropical Curves in Surfaces in 3-Space
| Autor: | Tristram Bogart, Eric Katz |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
General Mathematics
010102 general mathematics 0102 computer and information sciences 01 natural sciences Graph Combinatorics Mathematics - Algebraic Geometry 010201 computation theory & mathematics Algebraic torus 14T05 14C17 13P10 52A39 FOS: Mathematics Tropical geometry Mathematics - Combinatorics Combinatorics (math.CO) Algebraic curve 0101 mathematics Algebraic Geometry (math.AG) Physics::Atmospheric and Oceanic Physics Mathematics |
| Zdroj: | SIAM Journal on Discrete Mathematics. 26:1050-1067 |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/110825558 |
| Popis: | Tropicalization is a procedure that takes subvarieties of an algebraic torus to balanced weighted rational complexes in space. In this paper, we study the tropicalizations of curves in surfaces in 3-space. These are balanced rational weighted graphs in tropical surfaces. Specifically, we study the `lifting' problem: given a graph in a tropical surface, can one find a corresponding algebraic curve in a surface? We develop specific combinatorial obstructions to lifting a graph by reducing the problem to the question of whether or not one can factor a polynomial with particular support in the characteristic 0 case. This explains why some unusual tropical curves constructed by Vigeland are not liftable. 19 pages, 2 figures. Revised and reorganized, with a clearer focus on the nature of the combinatorial obstructions |
| Databáze: | OpenAIRE |
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