Reducible hyperplane sections of threefolds: two components of sectional genus zero

Abstract

By using adjunction theory, we describe the smooth complex projective threefolds admitting a simple normal crossing divisor of the form $A+B$ among their hyperplane sections, both components $A$ and $B$ being smooth surfaces with sectional genus $0$, and one of them being nef or at worst an exceptional divisor of the first reduction mapping.