algebraic manifold

Definition.

Let $k$ be a field and let $M\\subset k^{n}$ be a submanifold. $M$ is said tobe an algebraic manifold (or $k$ -algebraic) if there exists an irreducible algebraicvariety $V\\subset k^{n}$ such that $\\dim V=\\dim M$ and $M\\subset V$ . If $k=\\mathbb{R}$ ,then $M$ is called a Nash manifold.

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

References

1 M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild.,Princeton University Press,Princeton, New Jersey, 1999.

单词	AlgebraicManifold
释义	algebraic manifold Definition. Let $k$ be a field and let $M\\subset k^{n}$ be a submanifold. $M$ is said tobe an algebraic manifold (or $k$ -algebraic) if there exists an irreducible algebraicvariety $V\\subset k^{n}$ such that $\\dim V=\\dim M$ and $M\\subset V$ . If $k=\\mathbb{R}$ ,then $M$ is called a Nash manifold. It can be proved that such a manifold is defined as the zero set of a finite collection of analytic algebraic functions. References 1 M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild.,Princeton University Press,Princeton, New Jersey, 1999.
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