Generalized Donaldson–Thomas Invariants

Abstract

In the last chapter, we gave a definition of DT invariants on CY 3-folds when the moduli spaces of stable sheaves are fine and satisfy the ss=st condition. Although the first condition is not essential, the latter condition is much more essential, and it is much more difficult to define DT invariants when there exist strictly semistable sheaves. In this chapter, we explain the construction of DT invariants without the ss=st condition by Joyce–Song, using motivic Hall algebras.