Noether's theorem on rationality for surfaces

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.[1] See also Hirzebruch surface List of complex and algebraic surfaces References Castelnuovo’s Theorem Notes ^ Kurke, G. (1972). "The castelnuovo criterion of rationality" (PDF). Mathematical Notes of the Academy of Sciences of the USSR. 11: 20–23. doi:10.1007/BF01366911.[dead link] This algebraic geometry–related article is a stub. You can help Wikipedia by expanding it.

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