Nous donnons une condition suffisante pour que le groupe des automorphismes d'une variété complexe possède une structure de groupe de Lie. Comme application, nous obtenons que le groupe des automorphismes de tout domaine strictement pseudo-convexe ou de type pseudo-convexe fini a une structure de groupe de Lie.
We give a sufficient condition for complex manifolds for automorphism groups to become Lie groups. As an application, we see that the automorphism group of any strictly pseudoconvex domain or finite-type pseudoconvex domain has a Lie group structure.
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@article{CRMATH_2017__355_7_769_0, author = {Nagata, Yoshikazu}, title = {On the {Lie} group structure of automorphism groups}, journal = {Comptes Rendus. Math\'ematique}, pages = {769--773}, publisher = {Elsevier}, volume = {355}, number = {7}, year = {2017}, doi = {10.1016/j.crma.2017.06.007}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2017.06.007/} }
TY - JOUR AU - Nagata, Yoshikazu TI - On the Lie group structure of automorphism groups JO - Comptes Rendus. Mathématique PY - 2017 SP - 769 EP - 773 VL - 355 IS - 7 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.06.007/ DO - 10.1016/j.crma.2017.06.007 LA - en ID - CRMATH_2017__355_7_769_0 ER -
Nagata, Yoshikazu. On the Lie group structure of automorphism groups. Comptes Rendus. Mathématique, Tome 355 (2017) no. 7, pp. 769-773. doi : 10.1016/j.crma.2017.06.007. http://www.numdam.org/articles/10.1016/j.crma.2017.06.007/
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