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 $mathcal{V}={V_y}_{y in R^b}$ of real algebraic manifolds such that $V_0=V$, $mathcal{V}$ is an algebraic family of real algebraic manifolds over $y in R^b setminus {0}$ (possibly singular over $y=0$) and $mathcal{V}$ is perfectly parametrized by $R^b$ in the sense that $V_y$ is birationally nonisomorphic to $V_z$ for every $y,z in R^b$ with $y eq z$. A similar result continues to hold in the case in which $V$ is a singular real algebraic set.
On the principle of real moduli flexibility: perfect parametrizations / Ballico, Edoardo; Ghiloni, Riccardo. - In: ANNALES POLONICI MATHEMATICI. - ISSN 0066-2216. - STAMPA. - 111:3(2014), pp. 245-258. [10.4064/ap111-3-3]
On the principle of real moduli flexibility: perfect parametrizations
Ballico, Edoardo;Ghiloni, Riccardo
2014-01-01
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 $mathcal{V}={V_y}_{y in R^b}$ of real algebraic manifolds such that $V_0=V$, $mathcal{V}$ is an algebraic family of real algebraic manifolds over $y in R^b setminus {0}$ (possibly singular over $y=0$) and $mathcal{V}$ is perfectly parametrized by $R^b$ in the sense that $V_y$ is birationally nonisomorphic to $V_z$ for every $y,z in R^b$ with $y eq z$. A similar result continues to hold in the case in which $V$ is a singular real algebraic set.File | Dimensione | Formato | |
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