  The paper deals with a new sharp criterion ensuring the Aubin property of
solution maps to a class of parameterized variational systems. This class
includes parameter-dependent variational inequalities with non-polyhedral
constraint sets and also parameterized generalized equations with conic
constraints. The new criterion requires computation of directional limiting
coderivatives of the normal-cone mapping for the so-called critical directions.
The respective formulas have the form of a second-order chain rule and extend
the available calculus of directional limiting objects. The suggested procedure
is illustrated by means of examples.
