English

Toric and tropical compactifications of hyperplane complements

Algebraic Geometry 2014-12-01 v1 Combinatorics

Abstract

These lecture notes are based on lectures given by the author at the summer school "Arrangements in Pyr\'en\'ees" in June 2012. We survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gel'fand-MacPherson construction, Kapranov's visible contours compactification, and De Concini and Procesi's wonderful compactification. We explain how these constructions are unified by some ideas from the modern origins of tropical geometry. The paper contains a few new arguments intended to make the presentation as self-contained as possible.

Keywords

Cite

@article{arxiv.1306.3519,
  title  = {Toric and tropical compactifications of hyperplane complements},
  author = {Graham Denham},
  journal= {arXiv preprint arXiv:1306.3519},
  year   = {2014}
}

Comments

26 pages

R2 v1 2026-06-22T00:34:11.286Z