algebraic manifold


Let k be a field and let Mkn be a submanifoldMathworldPlanetmath. M is said to be an algebraic manifoldMathworldPlanetmath (or k-algebraicPlanetmathPlanetmath) if there exists an irreduciblePlanetmathPlanetmath algebraic variety Vkn such that dimV=dimM and MV. If k=, then M is called a Nash manifold.

It can be proved that such a manifoldMathworldPlanetmath is defined as the zero setPlanetmathPlanetmath of a finite collection of analytic algebraic functions.


  • 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
Title algebraic manifold
Canonical name AlgebraicManifold
Date of creation 2013-03-22 15:36:08
Last modified on 2013-03-22 15:36:08
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 6
Author jirka (4157)
Entry type Definition
Classification msc 14P20
Classification msc 14-00
Classification msc 58A07
Synonym algebraic submanifold
Synonym k-algebraic manifold
Synonym k-algebraic submanifold
Defines Nash manifold
Defines Nash submanifold