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.
Famous quotes containing the words theorem and/or surfaces:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)
“Footnotes are the finer-suckered surfaces that allow tentacular paragraphs to hold fast to the wider reality of the library.”
—Nicholson Baker (b. 1957)