Polarized interpolation and normal postulation for curves on Fano hypersurfaces - Ran, Ziv (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 514 A general hypersurface X of degree at most n in projective (n+1)-space contains curves C of any genus g≥ 0 and sufficiently large degree depending on g whose normal and conormal bundles in X have good postulation or natural cohomology in a sense that each twist has either H^0=0 or H^1=0. This implies a polarized version of the interpolation property for C on X.