On a rigidity criterion for del Pezzo fibrations over ${\mathbb P}^1$

Details On a rigidity criterion for del Pezzo fibrations over ${\mathbb P}^1$ On a rigidity criterion for del Pezzo fibrations over ${\mathbb P}^1$

1999-11-26

arxiv.org/abs/math/9911210v1

Mathematics

Algebraic Geometry

AmsLaTEX; 10 pages

Scientific paper

We discuss the rigidity problem for Mori fibrations on del Pezzo surfaces of
degree 1, 2 and 3 over ${\mathbb P}^1$ and formulate the following conjecture:
such a del Pezzo fibration $V/{\mathbb P}^1$ is birationally rigid if and only
if its quasi-effective and adjunction thresholds coincide. We prove the "only
if" part of this conjecture.

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