  This paper is devoted to present new error bounds of regularized gap
functions for polynomial variational inequalities with exponents explicitly
determined by the dimension of the underlying space and the number/degree of
the involved polynomials. The developed techniques are largely based on
variational analysis and semialgebraic geometry, which allow us to establish a
nonsmooth extension of the seminal \L ojasiewicz's gradient inequality to
regularized gap functions with explicitly calculated exponents.
