High Quality Content by WIKIPEDIA articles! In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle. In the Enriques-Kodaira classification of surfaces they form one of the 5 classes of surfaces of Kodaira dimension 0. Together with two-dimensional complex tori, they are the Calabi-Yau manifolds of dimension two. Most complex K3 surfaces are not algebraic. This means that they cannot be embedded in any projective space as a surface defined by polynomial equations. Andre Weil (1958) named them in honor of three algebraic geometers, Kummer, Kahler and Kodaira, and "la belle montagne K2 au Cachemire" (the beautiful mountain K2 in Kashmir).

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