On realizability of lines on tropical cubic surfaces and the Brundu-Logar normal form

2019/09/20 by Alheydis Geiger, Geiger, Alheydis
Mathematics · #14Q10 #14T05 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:14Q10 #msc:14T05

paper · pdf · doi:10.48550/arxiv.1909.09391

21 pages, 8 figures

arxiv created 2019/12/22 · arxiv updated 2019/12/24

Abstract

We present results on the relative realizability of infinite families of lines on general smooth tropical cubic surfaces. Inspired by the problem of relative realizability of lines on surfaces, we investigate the information we can derive tropically from the Brundu-Logar normal form of smooth cubic surfaces. In particular, we prove that for a residue field of characteristic ≠ 2 the tropicalization of the Brundu-Logar normal form is not smooth. We also take first steps in investigating the behavior of the tropicalized lines.

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