English

Tropical surface singularities

Algebraic Geometry 2013-09-04 v2 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1106.2676,
  title  = {Tropical surface singularities},
  author = {Hannah Markwig and Thomas Markwig and Eugenii Shustin},
  journal= {arXiv preprint arXiv:1106.2676},
  year   = {2013}
}

Comments

A gap in the classification was closed. 37 pages, 29 figures

R2 v1 2026-06-21T18:22:09.026Z