On fibrations and measures of irrationality of Hyper-Kahler manifolds

Claire Voisin ^[1]
1. [1] Institut de Mathématiques de Jussieu-Paris Rive Gauche, France
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 165-197
Idioma: inglés
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Resumen
- 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.