Zariski Geometries working seminar

Speaker

Adam Gutter, University of Waterloo

Abstract

Continuing an overview of Boris Zilber's textbook Zariski Geometries, we define geometrically motivated conditions on a topological (model-theoretic) structure, building towards a collection of conditions which will guarantee that the topological structure is in fact isomorphic to a smooth
algebraic curve over an algebraically closed field. In this seminar, we define the notion of "good dimension" that includes as an example, but is not limited to, the standard dimension of an algebraic variety. Using this notion, we define a class of model-theoretic objects known as Zariski Structures, which, as we shall see later, includes geometric objects found in algebraic, analytic, and differential geometry. Note: This seminar corresponds to section 3.1 of Zariski Geometries.