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Noether's theorem on rationality for surfaces : ウィキペディア英語版
Noether's theorem on rationality for surfaces
In mathematics, Noether's theorem on rationality for surfaces is a classical result of Max Noether on complex algebraic surfaces, giving a criterion for a rational surface. Let ''S'' be an algebraic surface that is non-singular and projective. Suppose there is a morphism φ from ''S'' to the projective line, with ''general fibre'' also a projective line. Then the theorem states that ''S'' is rational.〔http://www.springerlink.com/content/k855808570108741/fulltext.pdf?page=1〕
==See also==

*Hirzebruch surface
*List of complex and algebraic surfaces

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