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

Abstract

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