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[]
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]
Categories:
- Algebraic surfaces
- Theorems in algebraic geometry
- Algebraic geometry stubs