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, 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.

50 pages, to appear in Kyoto Journal of Math

References in corpus (1)

• Zero dimensional Donaldson-Thomas invariants of threefolds

Cited by in corpus (12)

• Holomorphic anomaly equations and the Igusa cusp form conjecture
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• The quantum tropical vertex
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Cohomological $\chi$-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
• Scattering diagrams, stability conditions, and coherent sheaves on ${\mathbb{P}}^2$
• Rank $r$ DT theory from rank $1$
• A proof of N.Takahashi's conjecture for $({\mathbb{P}}^2,E)$ and a refined sheaves/Gromov-Witten correspondence
• Twisted sheaves and $\mathrm{SU}(r)/{\mathbb{Z}}_r$ Vafa-Witten theory
• Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex
• Reduced Donaldson-Thomas invariants and the ring of dual numbers
• Resurgence and Riemann-Hilbert problems for elliptic Calabi-Yau threefolds