We prove that, under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines that have disconnected realization spaces.
@article{ASNSP_2012_5_11_4_921_0,
author = {Nazir, Shaheen and Yoshinaga, Masahiko},
title = {On the connectivity of the realization spaces of line arrangements},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {921--937},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 11},
number = {4},
year = {2012},
zbl = {06142478},
mrnumber = {3060685},
language = {en},
url = {http://archive.numdam.org/item/ASNSP_2012_5_11_4_921_0/}
}
TY - JOUR AU - Nazir, Shaheen AU - Yoshinaga, Masahiko TI - On the connectivity of the realization spaces of line arrangements JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 921 EP - 937 VL - 11 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_4_921_0/ LA - en ID - ASNSP_2012_5_11_4_921_0 ER -
%0 Journal Article %A Nazir, Shaheen %A Yoshinaga, Masahiko %T On the connectivity of the realization spaces of line arrangements %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 921-937 %V 11 %N 4 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_4_921_0/ %G en %F ASNSP_2012_5_11_4_921_0
Nazir, Shaheen; Yoshinaga, Masahiko. On the connectivity of the realization spaces of line arrangements. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 4, pp. 921-937. http://archive.numdam.org/item/ASNSP_2012_5_11_4_921_0/
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