Toric and tropical compactifications of hyperplane complements

Graham Denham

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 2, page 297-333
  • ISSN: 0240-2963

Abstract

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These lecture notes 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.

How to cite

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Denham, Graham. "Toric and tropical compactifications of hyperplane complements." Annales de la faculté des sciences de Toulouse Mathématiques 23.2 (2014): 297-333. <http://eudml.org/doc/275381>.

@article{Denham2014,
abstract = {These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gel$^\{\prime \}$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.},
author = {Denham, Graham},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {hyperplane arrangement; compactification; matroid; toric variety; visible contours; wonderful compactification},
language = {eng},
month = {3},
number = {2},
pages = {297-333},
publisher = {Université Paul Sabatier, Toulouse},
title = {Toric and tropical compactifications of hyperplane complements},
url = {http://eudml.org/doc/275381},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Denham, Graham
TI - Toric and tropical compactifications of hyperplane complements
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2014/3//
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 2
SP - 297
EP - 333
AB - These lecture notes survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we review the Gel$^{\prime }$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.
LA - eng
KW - hyperplane arrangement; compactification; matroid; toric variety; visible contours; wonderful compactification
UR - http://eudml.org/doc/275381
ER -

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