K3 surface

Common card · No. 402466

In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth, proper, geometrically connected algebraic surface that satisfies the same conditions. In the Enriques–Kodaira classification of surfaces, K3 surfaces form one of the four classes of minimal surfaces of Kodaira dimension zero. A simple example is the Fermat quartic surface x 4 + y 4 + z 4 + w 4 = 0 {\textstyle x^{4}+y^{4}+z^{4}+w^{4}=0} in complex projective 3-space. Together with two-dimensional compact complex tori, K3 surfaces are the Calabi–Yau manifolds (and...

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