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arXiv · 1905.00940

Birational self-maps of threefolds of (un)-bounded genus or gonality

Jérémy Blanc·Ivan Cheltsov·Alexander Duncan·Yuri Prokhorov
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Abstract

We study the complexity of birational self-maps of a projective threefold $X$ by looking at the birational type of surfaces contracted. These surfaces are birational to the product of the projective line with a smooth projective curve. We prove that the genus of the curves occuring is unbounded if and only if $X$ is birational to a conic bundle or a fibration into cubic surfaces. Similarly, we prove that the gonality of the curves is unbounded if and only if $X$ is birational to a conic bundle.

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Jérémy Blanc, Ivan Cheltsov, Alexander Duncan, Yuri Prokhorov. 2019-05-02. Birational self-maps of threefolds of (un)-bounded genus or gonality. https://arxiv.org/abs/1905.00940

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