On approximation of smooth submanifolds by nonsingular real algebraic subvarieties

Jacek Bochnak; Wojciech Kucharz

Displaying similar documents to “On approximation of smooth submanifolds by nonsingular real algebraic subvarieties”

Algebraic approximation of manifolds and spaces

A. Tognoli (1979-1980)

Séminaire Bourbaki

Similarity:

Embedding of real varieties and their subvarieties into Grassmannians.

M. A. Buchner (1995)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

Given a compact affine nonsingular real algebraic variety X and a nonsingular subvariety Z C X belonging to a large class of subvarieties, we show how to embed X in a suitable Grassmannian so that Z becomes the transverse intersection of the zeros of a section of the tautological bundle on the Grassmannian.

A note on global Nash subvarieties and Artin-Mazur theorem

Alessandro Tancredi, Alberto Tognoli (2004)

Bollettino dell'Unione Matematica Italiana

Similarity:

It is shown that every connected global Nash subvariety of $R^{n}$ is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.

Vector bundles over real algebraic surfaces and threefolds

Wojciech Kucharz (1986)

Compositio Mathematica

Similarity:

On homology classes represented by real algebraic varieties

Jacek Bochnak, Wojciech Kucharz (1998)

Banach Center Publications

Similarity:

Real algebraic structures on topological spaces

Selman Akbulut, Henry C. King (1981)

Publications Mathématiques de l'IHÉS

Similarity:

Counterexamples to representing homology classes by real algebraic subvarieties up to homeomorphism

R. Benedetti, M. Dedò (1984)

Compositio Mathematica

Similarity:

Codimension two transcendental submanifolds of projective space

Wojciech Kucharz, Santiago R. Simanca (2010)

Annales de l’institut Fourier

Similarity:

We provide a simple characterization of codimension two submanifolds of $ℙ^{n} (ℝ)$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n \geq 6$ . If the codimension two submanifold is a nonsingular algebraic subset of $ℙ^{n} (ℝ)$ whose Zariski closure in $ℙ^{n} (ℂ)$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in $ℙ^{n} (ℝ)$ .