Tropical surface singularities

Details Tropical surface singularities Tropical surface singularities

2011-06-14

arxiv.org/abs/1106.2676v1

Mathematics

Algebraic Geometry

36 pages, 29 figures

Scientific paper

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional 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 baricenters of certain faces of singular tropical surfaces, and, in some cases, there may be additional metric restrictions to faces of singular tropical surfaces.

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