On the commuting holomorphic endomorphisms of P^k

Details On the commuting holomorphic endomorphisms of P^k On the commuting holomorphic endomorphisms of P^k

2000-07-04

arxiv.org/abs/math/0007017v1

Mathematics

Complex Variables

42 pages, in French

Scientific paper

Let f_1, f_2 be holomorphic endomorphisms of P^k, of degrees d_1\geq 2, d_2\geq 2. Assume that f_1\circ f_2=f_2\circ f_1 and that d_1^{n_1}\not =d_2^{n_2} for all integers n_1, n_2. We then show that f_j are critically finite. Moreover there is an orbifold (P^k,n) such that f_1, f_2 are coverings of (P^k,n). In the P^2 case we give the list of commuting pairs satisfying the above conditions.

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