ABSTRACT
Assume that f:X×Y→Z is a map from the product of two affine varieties into another affine variety such that f is a regular map when one variable is fixed. We show that f is a regular map if the underlying field is not countably infinite. The condition is indispensable.
Mathematical Subject Classification:
ACKNOWLEDGMENT
The second author was partially supported by the National Natural Science Foundation of China.
Notes
#Communicated by L. Ein.