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Mathematics > Algebraic Geometry

arXiv:2201.07037 (math)
[Submitted on 18 Jan 2022 (v1), last revised 22 Aug 2022 (this version, v6)]

Title:On fibrations and measures of irrationality of hyper-Kähler manifolds

Authors:Claire Voisin
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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 $K3^{[2]}$. We extend his results to this more general context.
Comments: Final version
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:2201.07037 [math.AG]
  (or arXiv:2201.07037v6 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.07037
Journal reference: Revista de la Unión Matemática Argentina Vol. 64, No. 1, 2022, (special volume MCA) Pages 165-197

Submission history

From: Claire Voisin [view email]
[v1] Tue, 18 Jan 2022 15:03:44 UTC (30 KB)
[v2] Sat, 5 Feb 2022 12:49:38 UTC (30 KB)
[v3] Sat, 12 Feb 2022 08:44:02 UTC (30 KB)
[v4] Sun, 24 Apr 2022 08:52:18 UTC (31 KB)
[v5] Wed, 4 May 2022 12:43:18 UTC (32 KB)
[v6] Mon, 22 Aug 2022 13:17:35 UTC (32 KB)
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