The automorphism group of the Hilbert scheme of two points on a generic projective K3 surface
Samuel Boissi\`ere, Andrea Cattaneo, Marc Nieper-Wisskirchen and, Alessandra Sarti
TL;DR
This paper determines the automorphism group of the Hilbert scheme of two points on a generic projective K3 surface, revealing new examples of non-symplectic automorphisms linked to Pell's equation solutions.
Contribution
It provides the first comprehensive description of automorphisms for these Hilbert schemes, including non-natural non-symplectic automorphisms.
Findings
Automorphism group explicitly characterized
New examples of non-symplectic automorphisms identified
Automorphisms linked to solutions of Pell's equation
Abstract
We determine the automorphism group of the Hilbert scheme of two points on a generic projective K3 surface of any polarization. We obtain in particular new examples of Hilbert schemes of points having non-natural non-symplectic automorphisms. The existence of these automorphisms depends on solutions of Pell's equation.
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