The geometry of antisymplectic involutions, II
Abstract
We continue our study of fixed loci of antisymplectic involutions on projective hyper-Kähler manifolds of K3 [ n ] -type induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice. We prove that if the divisibility of the ample class is 2, then one connected component of the fixed locus is a Fano manifold of index 3, thus generalizing to higher dimensions the case of the LLSvS 8-fold associated to a cubic fourfold. We also show that, in the case of the LLSvS 8-fold associated to a cubic fourfold, the second component of the fixed locus is of general type, thus answering a question by Manfred Lehn.
Fields of Study & Subjects
Geometry and complex manifolds
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Journal de l’École polytechnique — Mathématiques
- Volume
- 13
- Pages
- 809–851
- Publication date
- 30 April 2026
- Language
- EN