On birational transformations of Hilbert schemes of points on K3 surfaces
Algebraic Geometry
2022-09-27 v3
Abstract
We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperk\"ahler birational model on which they become biregular. We also present new geometrical constructions of these automorphisms.
Keywords
Cite
@article{arxiv.2005.05187,
title = {On birational transformations of Hilbert schemes of points on K3 surfaces},
author = {Pietro Beri and Alberto Cattaneo},
journal= {arXiv preprint arXiv:2005.05187},
year = {2022}
}
Comments
18 pages. Exposition improved, review of the theory of Pell's equation moved to appendix. Remark 3.7 added, some minor results removed