Projective geometries of algebraically closed fields of characteristic zero

Annals of Pure and Applied Logic 60 (3):237-260 (1993)
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Abstract

Fix an algebraically closed field of characteristic zero and let G be its geometry of transcendence degree one extensions. Let X be a set of points of G. We show that X extends to a projective subgeometry of G exactly if the partial derivatives of the polynomials inducing dependence on its elements satisfy certain separability conditions. This analysis produces a concrete representation of the coordinatizing fields of maximal projective subgeometries of G

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Intersections of algebraically closed fields.C. J. Ash & John W. Rosenthal - 1986 - Annals of Pure and Applied Logic 30 (2):103-119.

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