Tropical Surface Singularities

Hannah Markwig, Thomas Markwig*, Eugenii Shustin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper, we study tropicalizations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional geometric type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and barycenters of certain faces of singular tropical surfaces, and, in some case, there may be additional metric restrictions to faces of singular tropical surfaces.

Original languageEnglish
Pages (from-to)879-914
Number of pages36
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - Dec 2012


FundersFunder number
Hermann-Minkowski Minerva Center for Geometry
Deutsche ForschungsgemeinschaftMA 4797/3-1
Deutsche Forschungsgemeinschaft
Israel Science Foundation448/09
Israel Science Foundation
Tel Aviv University


    • Discriminants
    • Regular subdivisions of lattice polytopes
    • Singularities
    • Tropical geometry


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