Unobstructedness of Deformations of Polarized Manifolds With Torsion Canonical Bundles

Let X be a smooth proper variety with a torsion canonical bundle over complex numbers and L be a line bundle on X. We prove the pair (X,L) is unobstructed if one of the following conditions is satisfied, (1)the line bundle L is ample, (2)the fundamental group $\pi_1(X)$ of X is finite.