K3 surface

Summary

A K3 surface is a smooth projective algebraic surface, or more generally a compact complex surface, with trivial canonical bundle and no holomorphic $1$-forms. K3 surfaces are the two-dimensional Calabi–Yau manifolds, the surface analogue of elliptic curves. All complex K3 surfaces are diffeomorphic to each other and simply connected, with second Betti number $22$. They are central in the classification of surfaces, in arithmetic geometry and in string theory.