On projective varieties admitting a bielliptic or trigonal curve-section

Abstract

We study smooth projective varieties X ⊆ PN of dimension n ≥ 3, such that for some linear (N-n+1)-dimensional space Π ⊆ PN, C=X∩Π is either a bielliptic or a trigonal curve. We give a description of X when deg ≥ 18 and when deg X ≤ 8.