Geometric models for the derived categories of Ginzburg algebras of n-angulated surfaces via local-to-global principles

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to as relative Ginzburg algebras, associated with marked surfaces equipped with a decomposition into $n$-gons ($n$-angulation). We relate their derived categories to the geometry of the surface. Results include the description of