The geometries of the Hrushovski constructions.

In 1993 in his paper "A new strongly minimal set" Hrushovski produced a family of counter examples to a conjecture by Zilber. Each one of these counter examples carry a pregeometry. We answer a question by Hrushovski about comparing these pregeometries and their localization to finite sets. We first analyse the pregeometries arising from different variations of the construction before the collapse. Then we compare the pregeometries of the family of new strongly minimal structures obtained after the collapse.