Differential forms, uniformization and the Kodaira problem

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The project consists of three parts. The first part, "Uniformization", is about characterizing algebraic varieties (or, more generally, complex spaces) that admit certain symmetries via numerical conditions (e.g. intersection numbers). The second part, "Kodaira problem", studies the question which (non-algebraic) compact Kähler manifolds can be deformed to algebraic varieties. This would mean that algebraic methods can be used to study such Kähler manifolds. The third part, "Differential forms", will investigate under which circumstances differential forms on singular spaces can be extended to a resolution of singularities. Since this problem is already well-understood over the complex numbers, we will concentrate on base fields of positive characteristic.