Generating functions of stable pair invariants via wall-crossings in derived categories

Understand

The notion of limit stability on Calabi-Yau 3-folds is introduced by the author to construct an approximation of Bridgeland-Douglas stability conditions at the large volume limit.

• It has also turned out that the wall-crossing phenomena of limit stable objects seem relevant to the rationality conjecture of the generating functions of Pandharipande-Thomas invariants.
• In this article, we shall make it clear how wall-crossing formula of the counting invariants of limit stable objects solves the above conjecture.