Stable pairs and BPS invariants

Understand

We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on Calabi-Yau 3-folds.

• The main tools are the theory of stable pairs in the derived category and Behrend's constructible function approach to the virtual class.
• We prove that for irreducible classes the stable pairs generating function satisfies the strong BPS rationality conjectures.
• We define the contribution of each curve to the BPS invariants.