Real Algebraic and Analytic Geometry
Submission: 2011, August 4.
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.
Full text, 31p.: dvi 217k, pdf 528k.