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

Mikhail Grinenko

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arXiv · math/9911210

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

Mikhail Grinenko

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Abstract

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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Mikhail Grinenko. 1999-11-26. On a rigidity criterion for del Pezzo fibrations over ${\mathbb P}^1$. https://arxiv.org/abs/math/9911210

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