Rational curves and strictly nef divisors on Calabi--Yau threefolds

We give a criterion for a nef divisor D to be semi-ample on a Calabi-Yau threefold X when D3=0=c2(X)⋅D and c3(X)≠0. As a direct consequence, we show that on such a variety X, if D is strictly nef and ν(D)≠1, then D is ample; we also show that if there exists a Cariter divisor D≢0 in the boundary of the nef cone of X, then X contains a rational curve when its topological Euler characteristic is not 0.