K3 surface

A K3 surface is an important and interesting example of a compact complex surface (complex dimension 2 being real dimension 4). Together with two dimensional complex tori, they are the Calabi-Yau manifolds of dimension two. Most K3 surfaces are not algebraic. This means that, in general, they cannot be embedded in any projective space as a surface defined by polynomial equations. However, K3 surfaces first arose in algebraic geometry and it is in this context that they received their name — it is after three algebraic geometers, Kummer, Kähler and Kodaira, alluding also to the mountain peak K2 in the news when the name was given during the 1950s.

Related Topics:
Compact - Calabi-Yau manifold - Algebraic geometry - Kummer - Kähler - Kodaira - K2

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