English

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