Noether's theorem on rationality for surfaces
In the modern world, Noether's theorem on rationality for surfaces has gained great relevance in all spheres of society. Its impact is reflected in people's lives, in the economic, political, cultural and technological spheres. Noether's theorem on rationality for surfaces is a topic that leaves no one indifferent, generating debate, reflection and action around it. Throughout history, Noether's theorem on rationality for surfaces has been a constant reference point, marking significant milestones and changes in the way we live and relate. In this article, we will explore different aspects and perspectives of Noether's theorem on rationality for surfaces, with the aim of better understanding its influence and reach in today's society.
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]
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Notes
- ^ Kurke, G. (1972). "The castelnuovo criterion of rationality". Mathematical Notes of the Academy of Sciences of the USSR. 11: 20–23. doi:10.1007/BF01366911.
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