We contribute to the classification of 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 particular, 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 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.
Non-symplectic automorphisms of odd prime order on manifolds of K3 [n] -type / C. Camere, A. Cattaneo, A. Cattaneo. - (2020). [Epub ahead of print]
|Titolo:||Non-symplectic automorphisms of odd prime order on manifolds of K3 [n] -type|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2020|
|Data ahead of print / Data di stampa:||7-feb-2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1017/nmj.2019.43|
|Appare nelle tipologie:||01 - Articolo su periodico|