  We consider an integer lattice quasiperiodic Schrodinger operator. The
underlying dynamics is either the skew-shift or the multi-frequency shift by a
Diophantine frequency. We assume that the potential function belongs to a
Gevrey class on the multi-dimensional torus. Moreover, we assume that the
potential function satisfies a generic transversality condition, which we show
to imply a Lojasiewicz type inequality for smooth functions of several
variables. Under these assumptions and for large coupling constant, we prove
that the associated Lyapunov exponent is positive for all energies, and
continuous as a function of energy, with a certain modulus of continuity.
Moreover, in the large coupling constant regime and for an asymptotically large
frequency - phase set, we prove that the operator satisfies Anderson
localization.
