Smooth tropical surfaces with infinitely many tropical lines

2007/03/22 by Magnus Dehli Vigeland, Vigeland, Magnus Dehli
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.math/0703682

27 pages, 12 figures. v2: Errors corrected, notation improved, referances added, Example 9.3 new

openalex publication_date 2007/03/22 · arxiv created 2007/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the tropical lines contained in smooth tropical surfaces in R³. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however, there exist smooth tropical surfaces of any degree with infinitely many tropical lines.

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