Integrality of Gopakumar-Vafa Invariants of Toric Calabi-Yau Threefolds

Details Integrality of Gopakumar-Vafa Invariants of Toric Calabi-Yau Threefolds Integrality of Gopakumar-Vafa Invariants of Toric Calabi-Yau Threefolds

2005-04-10

arxiv.org/abs/math/0504188v3

Mathematics

Algebraic Geometry

v1:33 pages; v2:typos corrected; v3: Proof of prop 3.3 given for general toric Calabi-Yau threefolds. The version to appear in

Scientific paper

The Gopakumar-Vafa invariants are numbers defined as certain linear combinations of the Gromov-Witten invariants. We prove that the GV invariants of a toric Calabi-Yau threefold are integers and that the invariants for high genera vanish. The proof of the integrality is based on elementary number theory and that of the vanishing uses the operator formalism and the exponential formula.

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