Definition: Affine repair problem

Let ${\mathcal{C}}_{\mathrm{ct}},{\mathcal{V}}_{\mathrm{def}}$ be complex vector spaces. A linear map

is the change in a defined defect produced by an admissible counterterm. For a fixed defect $D\in {\mathcal{V}}_{\mathrm{def}}$, the repair problem is

The obstruction class is

The quotient is algebraic unless a different meaning is explicitly declared.