nLab
K3 surface

Contents

Definition

A K3 surface is a Calabi-Yau variety of dimension 22. This means that the canonical bundle ω X= 2Ω X𝒪 X\omega_X=\wedge^2\Omega_X\simeq \mathcal{O}_X is trivial and H 1(X,𝒪 X)=0H^1(X, \mathcal{O}_X)=0.

Examples

  • A cyclic cover 2\mathbb{P}^2 branched over a curve of degree 66

  • A nonsingular degree 44 hypersurface in 3\mathbb{P}^3.

Basic Properties

References

Revised on April 11, 2014 02:06:05 by Urs Schreiber (185.37.147.12)