K

K3 surface A class of algebraic surface in abstract algebraic geometry, defined in a projective space over an algebraically closed field. In projective 3-space they can be regarded as deformations of quartic surfaces. A K3 surface is characterized as a nonsingular, nonrational surface, in several ways including:

(i.) irregularity, Kodaira dimension, and the canonical divisor are zero;

(ii.) irregularity is zero and the arithmetic, geometric, and first plurigenus are all one;

(iii.) as a compact complex analytic surface, the first Chern class is zero and it has Betti numbers b0 = 1, b1 = 0, b2 = 22, b3 = 0, b4 = 1.