Regular and rigid curves on some Calabi–Yau and general-type complete intersections

Let Formula: see text be either a general hypersurface of degree Formula: see text in Formula: see text or a general Formula: see text complete intersection in Formula: see text. We construct balanced rational curves on Formula: see text of all high enough degrees. If Formula: see text or Formula: see text, we construct rigid curves of genus Formula: see text on Formula: see text of all high enough degrees. As an application we construct some rigid bundles on Calabi–Yau threefolds. In addition, we construct some low-degree balanced rational curves on hypersurfaces of degree Formula: see text in Formula: see text.