Real Algebraic and Analytic Geometry |

The principle of moduli flexibility in Real Algebraic Geometry.

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Submission: 2011, August 4.

*Abstract:
Given a real closed field $R$, we define a real algebraic
manifold as an irreducible nonsingular algebraic subset of some $R^n$.
This paper is devoted to the notion of deformation of real algebraic
manifolds. The main purpose is to prove rigorously the validity of the
following informal 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. This principle extends to the singular case.*

Mathematics Subject Classification (2000): 14P05,14P20,14P25.

Keywords and Phrases: Real algebraic manifolds, Nash manifolds, algebraic real-deformations, algebro-Nash real-deformations.

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