On fibrations and measures of irrationality of hyper-K\"ahler manifolds

Claire Voisin

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arXiv · 2201.07037

On fibrations and measures of irrationality of hyper-K\"ahler manifolds

Claire Voisin

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Abstract

We prove some results on the fibers and images of rational maps from a hyper-K\"ahler manifold. We study in particular the minimal genus of fibers of a fibration into curves. The last section of this paper is devoted to the study of the rational map defined by a linear system on a hyper-K\"ahler fourfold satisfying numerical conditions similar to those considered by O'Grady in his study of fourfolds numerically equivalent to $K3^{[2]}$. We extend his results to this more general context.

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Claire Voisin. 2022-01-18. On fibrations and measures of irrationality of hyper-K\"ahler manifolds. https://arxiv.org/abs/2201.07037

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