On the principle of real moduli flexibility: perfect parametrizations

• Autorzy: Edoardo Ballico , Riccardo Ghiloni
• Języki publikacji: EN

Abstrakty

EN

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 $𝒱 = {V_y}_{y ∈ R^b}$ of real algebraic manifolds such that V₀ = V, 𝒱 is an algebraic family of real algebraic manifolds over $y ∈ R^b∖{0}$ (possibly singular over y = 0) and 𝒱 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.

Kategorie tematyczne

• 14P05: Real algebraic sets
• 14P25: Topology of real algebraic varieties
• 14P20: Nash functions and manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 111
• Numer: 3
• Strony: 245-258

Daty

wydano

2014

Twórcy

autor

Edoardo Ballico

• Department of Mathematics, University of Trento, 38123 Povo-Trento, Italy

autor

Riccardo Ghiloni

• Department of Mathematics, University of Trento, 38123 Povo-Trento, Italy

Identyfikatory

DOI

10.4064/ap111-3-3