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On the principle of real moduli flexibility: perfect parametrizations

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Ballico E., Ghiloni R.

Annales Polonici Mathematici

2014

tom 111

nr 3

245-258

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.

The principle of moduli flexibility for real algebraic manifolds

100%

Ballico E., Ghiloni R.

Annales Polonici Mathematici

2013

tom 109

nr 1

1-28

Given a real closed field R, we define a real algebraic manifold as an irreducible nonsingular algebraic subset of some Rⁿ. This paper deals with deformations of real algebraic manifolds. The main purpose is to prove rigorously the reasonableness of the following principle, which is in sharp contrast with the compact complex case: "The algebraic structure of every real algebraic manifold of positive dimension can be deformed by an arbitrarily large number of effective parameters".

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Ballico E.

2 Ghiloni R.

1 2014

1 2013

Wyniki wyszukiwania

On the principle of real moduli flexibility: perfect parametrizations

The principle of moduli flexibility for real algebraic manifolds