An elliptic surface is a smooth projective surface equipped with a surjective morphism to a smooth curve whose generic fiber is a smooth curve of genus one.
For an elliptic curve , projection is an elliptic fibration. Its canonical bundle is the pullback of , so it has no nonzero pluricanonical sections and its Kodaira dimension is .
Articles by others on the same topic
An elliptic surface is a type of algebraic surface that has a fibration structure, meaning it can be viewed as a family of elliptic curves. In more technical terms, an elliptic surface is a smooth projective surface \(S\) over a base scheme, typically taken to be the complex numbers, which admits a morphism to a base scheme \(B\) such that for every point in \(B\), the fiber over that point is an elliptic curve.