Abstract Let X be a connected complex projective manifold of dimension n ≥ 3. We describe those X containing an ample simple normal crossing divisor A 1 + A 2 such that both components A 1 and A 2 are Del Pezzo manifolds with respect to the polarization induced by L = [A 1 + A 2]. As consequence of this fact, when L is very ample, we complete the study of pairs (X, L) as above which admits a simple normal crossing divisor A 1 + A 2 ∈ |L| with Δ(Ai , LAi ) ≤ 1, where is the Δ-genus of the pair (Ai , LAi ) for i = 1, 2.

https://www.degruyter.com/view/j/form.2010.22.issue-4/forum.2010.037/forum.2010.037.pdf

Ample normal crossing divisors consisting of two Del Pezzo manifolds

Let X be an algebraic submanifold of the complex projective space
$\mathbb{P}^N$ of dimension $n \geq 5$. We describe those 
$X \subset \mathbb{P}^N$ whose intersection with some hyperplane is a smooth simply
normal crossing divisor $A_{1} + \cdots + A_{r}$ with $r \geq 2$ such that
$g(A_{k}, L_{A_k}) \leq 1$ for $k=1,\ldots, r$.

A. L. Tironi

Papers

High dimensional reducible hyperplane sections with multigenera $\leq$ 1