Kyoto Journal of Mathematics

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

Yukinobu Toda

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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.

Article information

Source
Kyoto J. Math., Volume 52, Number 1 (2012), 1-50.

Dates
First available in Project Euclid: 19 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1329684741

Digital Object Identifier
doi:10.1215/21562261-1503745

Mathematical Reviews number (MathSciNet)
MR2892766

Zentralblatt MATH identifier
1244.14047

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 18E30: Derived categories, triangulated categories

Citation

Toda, Yukinobu. Stability conditions and curve counting invariants on Calabi–Yau 3-folds. Kyoto J. Math. 52 (2012), no. 1, 1--50. doi:10.1215/21562261-1503745. https://projecteuclid.org/euclid.kjm/1329684741


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