On the space of real algebraic morphisms

Riccardo Ghiloni

Displaying similar documents to “On the space of real algebraic morphisms”

On the space of morphisms into generic real algebraic varieties

Riccardo Ghiloni (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let $Z$ be a real algebraic variety. We say that $Z$ is generic if there exist a finite family ${D_{i}}_{i = 1}^{n}$ of irreducible real algebraic curves with genus $\geq 2$ and a biregular embedding of $Z$ into the product variety $\prod_{i = 1}^{n} D_{i}$ . A bijective map $ϕ : {\tilde{Z}}^{} \to Z$ from a real algebraic variety $\tilde{Z}$ to $Z$ is called weak change of the algebraic structure of $Z$ if it is regular and its inverse is a Nash map. Generic real algebraic...

Algebraic approximation of manifolds and spaces

A. Tognoli (1979-1980)

Séminaire Bourbaki

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Some remarks about proper real algebraic maps

L. Beretta, A. Tognoli (2000)

Bollettino dell'Unione Matematica Italiana

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Nel presente lavoro si studiano le applicazioni polinomiali proprie $φ : R^{n} \to R^{q} .$ In particolare si prova: 1) se $φ : R^{n} \to R$ è un'applicazione polinomiale tale che $φ^{- 1} (y)$ è compatto per ogni $y \in R$ , allora $φ$ è propria; 2) se $φ : R^{n} \to R^{q}$ è polinomiale a fibra compatta e $φ (R^{n})$ è chiuso in $R^{q}$ allora $φ$ è propria; 3) l'insieme delle applicazioni polinomiali proprie di $R^{n}$ in $R^{q}$ è denso, nella topologia $C^{\infty}$ , nello spazio delle applicazioni $C^{\infty}$ di $R^{n}$ in $R^{q}$ .

On approximation of smooth submanifolds by nonsingular real algebraic subvarieties

Jacek Bochnak, Wojciech Kucharz (2003)

Annales scientifiques de l'École Normale Supérieure

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A note on global Nash subvarieties and Artin-Mazur theorem

Alessandro Tancredi, Alberto Tognoli (2004)

Bollettino dell'Unione Matematica Italiana

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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.

Non-uniruledness and the cancellation problem (II)

Robert Dryło (2007)

Annales Polonici Mathematici

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We study the following cancellation problem over an algebraically closed field of characteristic zero. Let X, Y be affine varieties such that $X \times^{m} ≅ Y \times^{m}$ for some m. Assume that X is non-uniruled at infinity. Does it follow that X ≅ Y? We prove a result implying the affirmative answer in case X is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces.