Symplectic involutions of K3[n]$K3^{[n]}$ type and Kummer n$n$ type manifolds. Issue 3 (15th April 2022)

• Record Type: Journal Article
• Authors: Kamenova, Ljudmila; Mongardi, Giovanni; Oblomkov, Alexei
• Is Part Of: Bulletin of the London Mathematical Society. Volume 54:Issue 3(2022)
• Page Start: 894
• Page End: 909
• Publication Date: 2022-04-15
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12594
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: In this paper, we describe the fixed locus of a symplectic involution on a hyper‐Kähler manifold of type K 3 [ n ] $K3^{[n]}$ or of Kummer n $n$ type. We prove that the fixed locus consists of finitely many copies of deformations of Hilbert schemes of K 3 $K3$ surfaces of lower dimensions and isolated fixed points.