Hostname: page-component-6bf8c574d5-2jptb Total loading time: 0 Render date: 2025-02-25T16:03:10.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytic cycles and generically finite holomorphic maps

Published online by Cambridge University Press:  17 April 2009

Yingchen Li
Yingchen Li
Affiliation:
Department of MathematicsUniversity of CaliforniaDavis CA 95616United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 457 - 460
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Ax, J., ‘The elementary theory of finite fields’, Ann. Math. (2) 88 (1968), 239–271.CrossRefGoogle Scholar
[2]Borel, A., ‘Injective endomorphisms of algebraic varieties’, Arch. Math. (Basel) 20 (1969), 531–537.CrossRefGoogle Scholar
[3]Grauert, H. and Remmert, R., Coherent analytic sheaves (Springer-Verlag, Berlin, Heidelberg, New York, 1984).CrossRefGoogle Scholar
[4]Kaup, L. and Kaup, B., Holomorphic functions (Walter de Gruyter, Berlin, New York, 1983).CrossRefGoogle Scholar
[5]Lojasiewicz, S., ‘Triangulation of semi-analytic set’, Ann. Scuola Norm. Super. Pisa 18 (1964), 449–474.Google Scholar