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La rigidite des invariants locaux des structures de Cauchy-Riemann reelles algebriques impose aux applications holomorphes des proprietes globales de rationalite (Poincare 1907), ou plus generalement d'algebricite (Webster 1977). Notre objectif principal sera d'unifier les resultats classiques ou recents, grâce a une etude du degre de transcendance, de discuter aussi l'hypothese habituelle de minimalite au sens de Tumanov, et ce en dimension quelconque, sans hypothese de rang et pour des applications holomorphes quelconques entre deux ensembles algebriques reels arbitraires.

On the partial algebraicity of holomorphic mappings between two real algebraic sets