Moduli of polarised varieties via canonical Kähler metrics
Abstract
Moduli spaces of polarised varieties (varieties together with an ample line bundle) are not Hausdorff in general. A basic goal of algebraic geometry is to construct a Hausdorff moduli space of some nice class of polarised varieties. I will discuss how one can achieve this goal using the theory of canonical Kähler metrics. In addition I will discuss some fundamental properties of this moduli space, for example the existence of a Weil-Petersson type Kähler metric. This is joint work with Philipp Naumann.