abstract: The purpose of this talk is to introduce the notion of limit stability on the category of perverse coherent sheaves on Calabi-Yau 3-folds, and construct new enumerative invariants of curves via limit stable objects. I will show that such invariants are generalizations of stable pair invariants introduced by Pandharipande and Thomas. I will show that investigations of wall-crossing phenomena of limit stable objects lead to the solution of the rationality conjecture of stable pair invariants.