Curve classes on Calabi–Yau complete intersections in toric varieties

Abstract We prove the integral Hodge conjecture for curve classes on smooth varieties of dimension at least three constructed as a complete intersection ample hypersurfaces in projective toric variety, such that anticanonical divisor is restriction nef divisor. In particular, this includes case Fano varieties. fact, using results Casagrande and minimal model program, we each case, generated by rational curves.