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The Automorphism Group of the Hilbert Scheme of Two Points on a Generic Projective K3 Surface

  • Samuel Boissiére
  • Andrea Cattaneo
  • Marc Nieper-Wisskirchen
  • Alessandra Sarti
Chapter
Part of the Progress in Mathematics book series (PM, volume 315)

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.

Keywords

Line Bundle Minimal Solution Hilbert Scheme Picard Number Ample Cone 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Samuel Boissiére
    • 1
  • Andrea Cattaneo
    • 2
  • Marc Nieper-Wisskirchen
    • 3
  • Alessandra Sarti
    • 1
  1. 1.Laboratoire de Mathématiques et ApplicationsUniversité de PoitiersFuturoscope Chasseneuil CedexFrance
  2. 2.Dipartimento di MatematicaUniversità di ParmaParmaItaly
  3. 3.Lehrstuhl für Algebra und ZahlentheorieAugsburgGermany

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