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

2007/01/18 by Shramov, Constantin
#14E05 #14E08 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0701521

Abstract

We prove a criterion of nonsingularity of a complete intersection of two fiberwise quadrics in a scroll over P¹. As a corollary we derive the following addition to the Alexeev theorem on rationality of standard Del Pezzo fibrations of degree 4 over P¹: we prove that any fibration of this kind with the topological Euler characteristic -4 is rational.

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