High dimensional reducible hyperplane sections with multigenera ≤ 1

摘要

Let X be an algebraic submanifold of the complex projective space P~N of dimension n ≥ 5. We describe those X is contained in P~N whose intersection with some hyperplane is a smooth simply normal crossing divisor A_1 + … + A_r with r ≥ 2 such that g (A_k, L_(A_K)) ≤ 1 for k = 1, …, r.