On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, and Riccardo Ghiloni. "On the principle of real moduli flexibility: perfect parametrizations." Annales Polonici Mathematici 111.3 (2014): 245-258. <http://eudml.org/doc/280691>.

@article{EdoardoBallico2014,
abstract = {Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $ = \{V_y\}_\{y ∈ R^b\}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y ∈ R^b∖\{0\}$ (possibly singular over y = 0) and is perfectly parametrized by $R^b$ in the sense that $V_y$ is birationally nonisomorphic to $V_z$ for every $y,z ∈ R^b$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic set.},
author = {Edoardo Ballico, Riccardo Ghiloni},
journal = {Annales Polonici Mathematici},
keywords = {Nash manifolds; real algebraic manifolds; purely real deformations},
language = {eng},
number = {3},
pages = {245-258},
title = {On the principle of real moduli flexibility: perfect parametrizations},
url = {http://eudml.org/doc/280691},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Edoardo Ballico
AU - Riccardo Ghiloni
TI - On the principle of real moduli flexibility: perfect parametrizations
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 3
SP - 245
EP - 258
AB - Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $ = {V_y}_{y ∈ R^b}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y ∈ R^b∖{0}$ (possibly singular over y = 0) and is perfectly parametrized by $R^b$ in the sense that $V_y$ is birationally nonisomorphic to $V_z$ for every $y,z ∈ R^b$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic set.
LA - eng
KW - Nash manifolds; real algebraic manifolds; purely real deformations
UR - http://eudml.org/doc/280691
ER -