Let f be a germ of biholomorphism of ℂ^n, fixing the origin. We show that if the germ commutes with a torus action, then we get information on the germs that can be conjugated to f, and furthermore on the existence of a holomorphic linearization or of a holomorphic normalization of f. We find out in a complete and computable manner what kind of structure a torus action must have in order to get a Poincaré-Dulac holomorphic normalization, studying the possible torsion phenomena. In particular, we link the eigenvalues of df_O to the weight matrix of the action. The link and the structure we found are more complicated than what one would expect; a detailed study was needed to completely understand the relations between torus actions, holomorphic Poincaré-Dulac normalizations, and torsion phenomena. We end the article giving an example of techniques that can be used to construct torus actions.
Raissy, J. (2009). Torus Actions in the Normalization Problem. THE JOURNAL OF GEOMETRIC ANALYSIS, 20(2), 472-524.
|Citazione:||Raissy, J. (2009). Torus Actions in the Normalization Problem. THE JOURNAL OF GEOMETRIC ANALYSIS, 20(2), 472-524.|
|Tipo:||Articolo in rivista - Articolo scientifico|
|Carattere della pubblicazione:||Scientifica|
|Titolo:||Torus Actions in the Normalization Problem|
|Data di pubblicazione:||set-2009|
|Rivista:||THE JOURNAL OF GEOMETRIC ANALYSIS|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s12220-009-9108-5|
|Appare nelle tipologie:||01 - Articolo su rivista|