Holomorphic linearization of commuting germs of holomorphic maps (Q375730)

In the paper under review, the author studies the problem of simultaneous linearization of a set \(f_1,...,f_h\) of formally linearizable germs of biholomorphisms of \(\mathbb{C}^n\) fixing the origin. Concerning the formal simultaneous linearization, she proves the following theorem: if \(f_1,...,f_h\) have almost simultaneously Jordanizable linear parts and commute pairwise, then they are simultaneously formally linearizable. Concerning the holomorphic simultaneous linearization, she introduces a simultaneous Brjuno condition and proves that if \(f_1,...,f_h\) have simultaneously diagonalizable linear parts and satisfy the simultaneous Brjuno condition, then they are holomorphically simultaneously linearizable if and only if they commute pairwise.