IJPAM: Volume 20, No. 2 (2005)

ITERATED COVERING MAPS IN FAMILIES
OF COMPACT COMPLEX SURFACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Here we consider (in the algebraic geometry set-up, too!) the existence of families of data $(T,\{X_t\}_{t\in T},s: T \in T,\{f_t\}_{t\in T})$ such that:

(i)
$T$ is a reduced and irreducible complex space;
(ii)
$\{X_t\}_{t\in T}$ is a smooth family of connected and compact complex manifolds;
(iii)
$s: T \to T$ is a set-theoretic map;
(iv)
$f_t: X_{s(t)} \to X_t$ is a locally invertible, but not globally invertible analytic map.


Received: March 15, 2005

AMS Subject Classification: 14J25, 14H20, 32J15

Key Words and Phrases: self-map, ètale map, compact complex surface, singular projective curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 2