Tropical Surface Singularities
Tropical Surface Singularities
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热带表面奇点
DOI：
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发表时间：
2011
影响因子：
0.8
通讯作者：
E. Shustin
中科院分区：
文献类型：
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作者：
H. Markwig;Thomas Markwig;E. Shustin
本文研究了环三折中奇异曲面的热带化问题。我们对极大维几何类型的热带奇异曲面进行了完全分类，证明了它们一般只能有有限多个奇点，并刻画了奇点的所有可能位置。更准确地说，我们证明了奇点必须是奇异热带曲面某些面的顶点或广义中点和重心，并且在某些情况下，对奇异热带曲面的面可能存在额外的度量限制。
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.