On the space of real algebraic morphisms

Ghiloni, Riccardo. "On the space of real algebraic morphisms." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.4 (2003): 307-317. <http://eudml.org/doc/252272>.

@article{Ghiloni2003,
abstract = {In this Note, we announce several results concerning basic properties of the spaces of morphisms between real algebraic varieties. Our results show a surprising intrinsic rigidity of Real Algebraic Geometry and illustrate the great distance which, in some sense, exists between this geometry and Real Nash one. Let us give an example of this rigidity. An affine real algebraic variety $X$ is rigid if, for each affine irreducible real algebraic variety $Z$, the set of all nonconstant regular morphisms from $Z$ to $X$ is finite. We are able to prove that, given a compact smooth manifold $M$ of positive dimension, there exists an uncountable family $\\{ M_\{i\}\\}_\{i \in I\}$ of rigid affine nonsingular real algebraic varieties diffeomorphic to $M$ such that, for each $i \neq j$ in $I$, $M_\{i\}$ is not biregularly isomorphic to $M_\{j\}$.},
author = {Ghiloni, Riccardo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Real algebraic morphisms; Real algebraic rigidity; Arithmetic of dominating real alge- braic morphisms; Arithmetic of dominating real algebraic morphisms},
language = {eng},
month = {12},
number = {4},
pages = {307-317},
publisher = {Accademia Nazionale dei Lincei},
title = {On the space of real algebraic morphisms},
url = {http://eudml.org/doc/252272},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Ghiloni, Riccardo
TI - On the space of real algebraic morphisms
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/12//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 4
SP - 307
EP - 317
AB - In this Note, we announce several results concerning basic properties of the spaces of morphisms between real algebraic varieties. Our results show a surprising intrinsic rigidity of Real Algebraic Geometry and illustrate the great distance which, in some sense, exists between this geometry and Real Nash one. Let us give an example of this rigidity. An affine real algebraic variety $X$ is rigid if, for each affine irreducible real algebraic variety $Z$, the set of all nonconstant regular morphisms from $Z$ to $X$ is finite. We are able to prove that, given a compact smooth manifold $M$ of positive dimension, there exists an uncountable family $\{ M_{i}\}_{i \in I}$ of rigid affine nonsingular real algebraic varieties diffeomorphic to $M$ such that, for each $i \neq j$ in $I$, $M_{i}$ is not biregularly isomorphic to $M_{j}$.
LA - eng
KW - Real algebraic morphisms; Real algebraic rigidity; Arithmetic of dominating real alge- braic morphisms; Arithmetic of dominating real algebraic morphisms
UR - http://eudml.org/doc/252272
ER -