Stability conditions and curve counting invariants on Calabi-Yau 3-folds

Abstract

The purpose of this paper is twofold. First we give a survey on the recent developments of curve counting invariants on Calabi-Yau 3-folds, for example, Gromov- Witten theory, Donaldson-Thomas theory, and Pandharipande-Thomas theory. Next we focus on the proof of the rationality conjecture of the generating series of PT invariants and discuss its conjectural Gopakumar-Vafa form. © 2012 by Kyoto University.