Elliptic surface

In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper connected smooth morphism to an algebraic curve, almost all of whose fibers are elliptic curves. The fibers that are not elliptic curves are called the singular fibers and were classified by Kunihiko Kodaira. Elliptic surfaces form a large class of surfaces that contains many of the interesting examples of surfaces, and are relatively well-understood from the viewpoint of complex manifold theory and the theory of smooth 4-manifolds. They are similar to (have analogies with, that is), elliptic curves over number fields.
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