In this partly expository note we construct Teichmüller space by patching together Kuranishi families. We also discuss the basic properties of Teichmüller space, and in particular show that our construction leads to simplifications in the proof of Teichmüller’s theorem asserting that the genus Teichmüller space is homeomorphic to a -dimensional ball.
@article{ASNSP_2009_5_8_1_89_0,
author = {Arbarello, Enrico and Cornalba, Maurizio},
title = {Teichm\"uller space via {Kuranishi} families},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {89--116},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {1},
year = {2009},
mrnumber = {2512202},
zbl = {1186.30041},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_1_89_0/}
}
TY - JOUR AU - Arbarello, Enrico AU - Cornalba, Maurizio TI - Teichmüller space via Kuranishi families JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 89 EP - 116 VL - 8 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_1_89_0/ LA - en ID - ASNSP_2009_5_8_1_89_0 ER -
%0 Journal Article %A Arbarello, Enrico %A Cornalba, Maurizio %T Teichmüller space via Kuranishi families %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 89-116 %V 8 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2009_5_8_1_89_0/ %G en %F ASNSP_2009_5_8_1_89_0
Arbarello, Enrico; Cornalba, Maurizio. Teichmüller space via Kuranishi families. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, pp. 89-116. http://www.numdam.org/item/ASNSP_2009_5_8_1_89_0/
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