Categorical Wall-Crossing via Koszul Duality

The main result in this chapter is to prove Conjecture 4.3.14 when \(\beta \) is an irreducible curve class. In this case, we can also describe the semiorthogonal complement of the fully-faithful functor, which recovers the wall-crossing formula of the PT invariants, and also gives a rationality statement of the generating series of PT categories in the Grothendieck group of triangulated categories.