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1936-1944
On fibrations and measures of irrationality of hyper-Khäler manifolds
Volume 64, no. 1 (2022), pp. 165–197

Abstract

We prove some results on the fibers and images of rational maps from a hyper-Kähler 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-Kähler fourfold satisfying numerical conditions similar to those considered by O'Grady in his study of fourfolds numerically equivalent to $\mathrm{K}3^{[2]}$. We extend his results to this more general context.