Analytic cycles and generically finite holomorphic maps
1995 ◽
Vol 52
(3)
◽
pp. 457-460
Keyword(s):
We study the behaviour of analytic cycles under generically finite holomorphic mappings between compact analytic spaces and prove that if two compact and normal complex analytic spaces have the same analytic homology groups, then any generically one to one holomorphic map between them must be a biholomorphic mapping. This generalises an old theorem of Ax and Borel.