Fixed loci of symplectic automorphisms of K3^[n] and n-Kummer type manifolds

2023/08/28 by Ljudmila Kamenova, Giovanni Mongardi, Kamenova, Ljudmila +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2308.14692

openalex publication_date 2023/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces and for generalized Kummer varieties. Here we extend our previous results from the case of involutions to more general groups. In particular, under some conditions on the dimension, we give the full answer for finite group actions of symplectic automorphisms coming from K3 surfaces. We prove that the all irreducible components of the fixed loci are of K3^[k] type of lower dimensions or isolated points.

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• In search of maximal branes on hyper-Kähler manifolds

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• Symplectic involutions of K3^[n] type and Kummer n type manifolds
• Towards a classification of symplectic automorphisms on manifolds of K3^[n] type
• Automorphisms of hyperkähler manifolds
• Finite groups of symplectic automorphisms of hyperkähler manifolds of type K3^[2]
• Terminalizations of quotients of compact hyperkähler manifolds by induced symplectic automorphisms