K3 Surface - Examples

Examples

  • A double cover of the projective plane branched along a non-singular degree 6 curve is a genus 2 K3 surface.
  • A Kummer surface is the quotient of a two-dimensional abelian variety A by the action a → −a. This results in 16 singularities, at the 2-torsion points of A. The minimal resolution of this quotient is a genus 3 K3 surface.
  • A non-singular degree 4 surface in P3 is a genus 3 K3 surface.
  • The intersection of a quadric and a cubic in P4 gives genus 4 K3 surfaces.
  • The intersection of three quadrics in P5 gives genus 5 K3 surfaces.
  • Brown (2007) describes a computer database of K3 surfaces.

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