UC Riverside

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].