Dans ces notes, nous passons en revue puis comparons diverses compactifications d’un complément d’un arrangement d’hyperplans complexes. En particulier, nous examinons la construction de Gelfand-MacPherson, la compactification des contours visibles de Kapranov, et la compactification merveilleuse de De Concini et Procesi. Nous expliquons comment ces constructions sont unifiées par quelques idées provenant des origines modernes de la géométrie tropicale.
These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gelfand-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.
@article{AFST_2014_6_23_2_297_0,
author = {Graham Denham},
title = {Toric and tropical compactifications of hyperplane complements},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {297--333},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {2},
year = {2014},
doi = {10.5802/afst.1408},
mrnumber = {3205595},
zbl = {06297894},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1408/}
}
TY - JOUR AU - Graham Denham TI - Toric and tropical compactifications of hyperplane complements JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2014 SP - 297 EP - 333 VL - 23 IS - 2 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1408/ DO - 10.5802/afst.1408 LA - en ID - AFST_2014_6_23_2_297_0 ER -
%0 Journal Article %A Graham Denham %T Toric and tropical compactifications of hyperplane complements %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2014 %P 297-333 %V 23 %N 2 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1408/ %R 10.5802/afst.1408 %G en %F AFST_2014_6_23_2_297_0
Graham Denham. Toric and tropical compactifications of hyperplane complements. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro Spécial à l’occasion de la conférence Arrangements in Pyrénées, Pau 11-15 juin 2012, Tome 23 (2014) no. 2, pp. 297-333. doi : 10.5802/afst.1408. https://afst.centre-mersenne.org/articles/10.5802/afst.1408/
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