In
mathematics, in the field of
complex manifolds, 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, in a definite sense, 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.
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