Do Duc Thai (aus Hanoi)
Title: Finiteness of meromorphic mappings.
Abstract: The purpose of this talks is to present unicity problem with truncated
multiplicities of meromorphic mappings in several complex variables.
In 1926, R. Nevanlinna showed that, for two distinct nonconstant meromorphic functions
$f$ and $g$ on the complex plane $\C$, they cannot have the same inverse images for
five distinct values, and $g$ is a special type of linear fractional transformation
of $f$ if they have the same inverse images counted with multiplicities for four
distinct values.
Over the last few decades, there have been several results for generalizing the above
theorem of Nevanlinna to the case of meromorphic mappings of $\C^n$ into the complex
projective space $\P^N(\C).$
The unicity problem without truncated mutiplicities has grown into a huge theory.
Unfortunately, it is a difficult open question if truncated counting functions can
be arised in this theory. There are only a few of such results in some restricted
situations. The main purpose of this talks is to formulate the best results available
at present for two cases in which the targets are hyperplanes and the targets are
hypersurfaces.