TY - JOUR
T1 - Tropical Surface Singularities
AU - Markwig, Hannah
AU - Markwig, Thomas
AU - Shustin, Eugenii
N1 - Funding Information:
We would like to thank Christian Haase for useful discussions. The images were obtained with the aid of Polymake [], Javaview [], jReality [], tropicalinsect [], xfig and texdraw. The authors were supported by the Hermann-Minkowski Minerva Center for Geometry at the Tel Aviv University, and by the DFG-grant MA 4797/3-1 as part of the priority program SPP 1489. The third author was also supported by the Israeli Science Foundation grant no. 448/09. We would like to thank an anonymous referee for valuable comments on a first draft of this paper.
PY - 2012/12
Y1 - 2012/12
N2 - 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.
AB - 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.
KW - Discriminants
KW - Regular subdivisions of lattice polytopes
KW - Singularities
KW - Tropical geometry
UR - http://www.scopus.com/inward/record.url?scp=84870332555&partnerID=8YFLogxK
U2 - 10.1007/s00454-012-9453-1
DO - 10.1007/s00454-012-9453-1
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AN - SCOPUS:84870332555
SN - 0179-5376
VL - 48
SP - 879
EP - 914
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 4
ER -