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In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex numbers, these fibers are elliptic curves, perhaps without a chosen origin.) The surface and the base curve are assumed to be non-singular (complex manifolds or regular schemes, depending on the context). The fibers that are not elliptic curves are called the singular fibers and were classified by Kunihiko Kodaira. Both elliptic and singular fibers are important in string theory, especially in F-theory. Elliptic surfaces form a large class of surfaces that contains many of the interesting examples of surfaces, and are relatively well-understood in the theories of complex manifolds and smooth 4-manifolds. They are similar to (have analogies with, that is), elliptic curves over number fields. ==Examples== *The product of any elliptic curve with any curve is an elliptic surface (with no singular fibers). *All surfaces of Kodaira dimension 1 are elliptic surfaces. *Every complex Enriques surface is elliptic, and has an elliptic fibration over the projective line. *Kodaira surfaces *Dolgachev surfaces *Shioda modular surfaces 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「elliptic surface」の詳細全文を読む スポンサード リンク
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