Moduli Spaces for Special Surfaces of General Type

Classification of algebraic varieties consists of two parts: First find a set of discrete invariants like dimensions, genera, … to describe the basic topological properties of the variety, and then try to make the set of all varieties with given discrete invariants into an algebraic variety, the so called moduli space. The prototypical example is classification of Riemann surfaces: The genus is sufficient to fix the topological (and even differentiable) structure, and the set of all Riemann surfaces of a given genus can be made into an irreducible quasi-projective variety; its dimension is 3g — 3 for g ≥ 2.