On rationality of nonsingular threefolds with a pencil of Del Pezzo surfaces of degree 4

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122219We prove a criterion of nonsingularity of a complete intersection of two fiberwise quadrics in a scroll over $P^1$. As a corollary we derive the following addition to the Alexeev theorem on rationality of standard Del Pezzo fibrations of degree 4 over $P^1$: we prove that any fibration of this kind with the topological Euler characteristic -4 is rational.13 pagesAlgebraic Geometry14E08; 14E05On rationality of nonsingular threefolds with a pencil of Del Pezzo surfaces of degree 4text