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

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

2011-03-22

arxiv.org/abs/1103.4229v2

Mathematics

Algebraic Geometry

50 pages, to appear in Kyoto Journal of Math

Scientific paper

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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