A class of counter-examples to the hypersection problem based on forcing equations

Abstract.

We give a class of three-dimensional Stein spacesW together with a hypersurface H, such that the complement W - H is not Stein, but such that for every analytic surface $S \subset W$ the complement $S - S \cap H$ is Stein. This class is constructed using forcing equations and gives new counter-examples to the hypersection problem.