Projective manifolds with hyperplane sections being five-sheeted covers of projective space

摘要

Let L be a very ample line bundle on a smooth complex projective variety X of dimension ≥ 7. We classify the polarized manifolds (X, V) such that there exists a smooth member A of |L| endowed with a branched covering of degree five π : A → P~n. The cases of deg π = 2 and 3 are already studied by Lanteri-Palleschi-Sommese.