Stability conditions and curve counting invariants on Calabi-Yau 3-folds
Yukinobu Toda
TL;DR
This paper surveys recent advances in curve counting invariants on Calabi-Yau 3-folds and proves the rationality conjecture for PT invariants, discussing their Gopakumar-Vafa structure.
Contribution
It provides a comprehensive survey and proves the rationality of PT invariants' generating series, linking them to Gopakumar-Vafa conjectures.
Findings
Proof of the rationality conjecture for PT invariants
Discussion of Gopakumar-Vafa conjectural structure
Summary of recent developments in curve counting invariants
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, e.g. 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.
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