English

Rational surfaces with a non-arithmetic automorphism group

Algebraic Geometry 2024-10-14 v3

Abstract

In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples YY are Looijenga pairs, i.e., there is a connected singular nodal curve DYD \subset Y such that KY+D=0K_{Y} + D = 0.

Keywords

Cite

@article{arxiv.2310.08768,
  title  = {Rational surfaces with a non-arithmetic automorphism group},
  author = {Jennifer Li and Sebastián Torres},
  journal= {arXiv preprint arXiv:2310.08768},
  year   = {2024}
}

Comments

Final version. To appear in the Bulletin of the London Mathematical Society

R2 v1 2026-06-28T12:49:22.309Z