Proper holomorphic mappings

Abstract

Let us recall that a mapping F: X -* Y is proper if ~1(A') is a compact subset of X whenever K c Y is compact. If X and Y are complex spaces, and if F: X -> Y is a proper holomorphic mapping, then F~(y 0 ) is a compact analytic subvariety of X for all points y 0 e Y. Proper mappings between complex spaces were studied from the general point of view of complex spaces in the 1950s and early 60s (see ). Two results from this era are a factorization theorem of Stein [88] and the Remmert Proper Mapping theorem: Iff: X -> Y is a proper mapping, and if S c X is a subvariety ofX 9 then f (S) is a subvariety of Y.