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

1. ^ http://www.springerlink.com/content/k855808570108741/fulltext.pdf?page=1

This algebra-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Algebra stubs Algebraic surfaces Theorems in geometry Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Judge Dredd (role-playing game) Lake Grove, Oregon Look at other dictionaries: Max Noether's theorem — In mathematics, Max Noether s theorem in algebraic geometry may refer to at least six results of Max Noether. Noether s theorem usually refers to a result derived from work of his daughter Emmy Noether. There are several closely related results… …   Wikipedia Max Noether — Born September 24, 1844(1844 09 24 …   Wikipedia List of mathematics articles (N) — NOTOC N N body problem N category N category number N connected space N dimensional sequential move puzzles N dimensional space N huge cardinal N jet N Mahlo cardinal N monoid N player game N set N skeleton N sphere N! conjecture Nabla symbol… …   Wikipedia Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”