On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico; Riccardo Ghiloni

Annales Polonici Mathematici, Tome 111 (2014), p. 245-258 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $= {V_{y}}_{y \in R^{b}}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y \in R^{b} ∖ 0$ (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 $y, z \in R^{b}$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic set.

Publié le : 2014-01-01

Zbl 1308.14061

EUDML-ID : urn:eudml:doc:280691

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-3-3,
     author = {Edoardo Ballico and Riccardo Ghiloni},
     title = {On the principle of real moduli flexibility: perfect parametrizations},
     journal = {Annales Polonici Mathematici},
     volume = {111},
     year = {2014},
     pages = {245-258},
     zbl = {1308.14061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-3-3}
}

Edoardo Ballico; Riccardo Ghiloni. On the principle of real moduli flexibility: perfect parametrizations. Annales Polonici Mathematici, Tome 111 (2014) pp. 245-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap111-3-3/