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

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

2007-01-18

arxiv.org/abs/math/0701521v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

We 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.

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