Errata-Corrige : “Iteration theory, compactly divergent sequences and commuting holomorphic maps”

A NNALI DELLA

S ^CUOLA N ^ORMALE S UPERIORE DI P ^ISA Classe di Scienze

M ^ARCO A ^BATE

Errata-Corrige : “Iteration theory, compactly divergent sequences and commuting holomorphic maps”

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 4

^e

série, tome 18, n

^o

4 (1991), p. 631

<http://www.numdam.org/item?id=ASNSP_1991_4_18_4_631_0>

© Scuola Normale Superiore, Pisa, 1991, tous droits réservés.

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Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

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Errata-Corrige

Iteration Theory, Compactly Divergent Sequences

and

Commuting Holomorphic Maps

MARCO ABATE

Serie

IV, 18,

²

(1991)

pp. 167-191.

Page 182,

^{in the statement of Theorem 2.17 the}

hypothesis

(0)

for

^all

odd j

^{should be}

replaced by (0) for

^all

positive j, ^i.e., by

D is

acyclic.

^{The theorem} may be true in

general,

^{but the}

proof

described in the paper works

only

under this more restrictive

hypothesis (the

^{trouble lies in}

the

application

^of the Lefschetz fixed

point

^{theorem at the end of the}

proof).

Page 169,

^{in the}

preprint Holomorphic

^{actions on} contractible domains without

fixed points, by

^{M. Abate and P.}

Heinzner,

it is described a bounded

pseudoconvex

contractible taut domain in

C 8 where Zpq

^acts

holomorphically

without fixed

points.

^{This means}

^that,

ⁱⁿ

general,

^the

conjecture

^{stated in the}

paper is false: there are

holomorphic self-maps

^of contractible taut manifolds with

periodic points

and without fixed

points.

^{Thus the statement of Theorem}

0.4 is the best

possible.

^The

conjecture

^is still open for

holomorphic self-maps

of contractible

strongly pseudoconvex

^domains.