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Non-symplectic automorphisms of odd prime order on manifolds of\n K3[n]-type

2018/02/01 by Chiara Camere, Camere, Chiara, Alberto Cattaneo +2
Mathematics · #14C05 #14C34 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1802.00192

openalex publication_date 2018/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify non-symplectic automorphisms of odd prime order on irreducible\nholomorphic symplectic manifolds which are deformations of Hilbert schemes of\nany number n of points on K3 surfaces, extending results already known for n=2.\nIn order to do so, we study the properties of the invariant lattice of the\nautomorphism (and its orthogonal complement) inside the second cohomology\nlattice of the manifold. We also explain how to construct automorphisms with\nfixed action on cohomology: in the cases n=3,4 the examples provided allow to\nrealize all admissible actions in our classification. For n=4, we present a\nconstruction of non-symplectic automorphisms on the Lehn-Lehn-Sorger-van\nStraten eightfold, which come from automorphisms of the underlying cubic\nfourfold.\n

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