2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149987Let $g : X \to Y$ be the contraction of an extremal ray of a smooth projective 4-fold $X$ such that $\dim Y=3$. Then $g$ may have a finite number of 2-dimensional fibers. We shall classify those fibers. Especially we shall prove that any two points of such a fiber is joined by a chain of rational curves of length at most 2 with respect to $-K_X$, and that $|-K_X|$ is $g\text{-free}$.65 pages, TeX dialect: amspptAlgebraic Geometrytext