  The paper is devoted to exact and asymptotic formulas for the determinants of
Toeplitz matrices with perturbations by blocks of fixed size in the four
corners. If the norms of the inverses of the unperturbed matrices remain
bounded as the matrix dimension goes to infinity, then standard perturbation
theory yields asymptotic expressions for the perturbed determinants. This
premise is not satisfied for matrices generated by so-called Fisher-Hartwig
symbols. In that case we establish formulas for pure single Fisher-Hartwig
singularities and for Hermitian matrices induced by general Fisher-Hartwig
symbols.
