Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

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


Cattaneo,  Alberto
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

(Preprint), 490KB

Supplementary Material (public)
There is no public supplementary material available

Camere, C., & Cattaneo, A. (2020). Non-symplectic automorphisms of odd prime order on manifolds of K3[n]-type. Manuscripta Mathematica, 163(3-4), 299-342. doi:10.1007/s00229-019-01163-4.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9E63-9
We classify non-symplectic automorphisms of odd prime order on irreducible holomorphic symplectic manifolds which are deformations of Hilbert schemes of any number n of points on K3 surfaces, extending results already known for n=2.
In order to do so, we study the properties of the invariant lattice of the automorphism (and its orthogonal complement) inside the second cohomology lattice of the manifold. We also explain how to construct automorphisms with fixed action on cohomology: in the cases n=3,4 the examples provided allow to realize all admissible actions in our classification. For n=4, we present a construction of non-symplectic automorphisms on the Lehn-Lehn-Sorger-van Straten eightfold, which come from automorphisms of the underlying cubic fourfold.