Projective planes in algebraically closed fields - Evans,DM; Hrushovski,E (Proceedings of the London Mathematical Society, 1991)
We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particular configuration of four lines and six points in the geometry indicates the presence of a connected one-dimensional algebraic group. © 1991 Oxford University Press.