Curve counting theories via stable objects I. DT/PT correspondence

Understand

The Donaldson-Thomas invariant is a curve counting invariant on Calabi-Yau 3-folds via ideal sheaves.

• Another counting invariant via stable pairs is introduced by Pandharipande and Thomas, which counts pairs of curves and divisors on them.
• These two theories are conjecturally equivalent via generating functions, called DT/PT correspondence.
• In this paper, we show the Euler characteristic version of DT/PT correspondence, using the notion of weak stability conditions and the wall-crossing formula.