Some Observations on Gopakumar-Vafa Invariants of Some Local Calabi-Yau Geometries

Zhou, Jian

doi:10.1142/9789812772527_0048

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Some Observations On Gopakumar-vafa Invariants1

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2010

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“…As observed in [28], M (d, g, k) are much smaller and have some nice properties. Starting from Table 1, we get Table 2 for M (2, g, k).…”

Section: Some Observations On Gopakumar-vafa Invariantsmentioning

confidence: 59%

Local Gromov-Witten invariants and tautological sheaves on Hilbert schemes

Yang

Zhou

2010

Sci. China Math.

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We study the local Gromov-Witten invariants of O(k) ⊕ O(−k − 2) → P 1 by localization techniques and the Mariño-Vafa formula, using suitable circle actions. They are identified with the equivariant RiemannRoch indices of some power of the determinant of the tautological sheaves on the Hilbert schemes of points on the affine plane. We also compute the corresponding Gopakumar-Vafa invariants and make some conjectures about them.

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“…As observed in [28], M (d, g, k) are much smaller and have some nice properties. Starting from Table 1, we get Table 2 for M (2, g, k).…”

Section: Some Observations On Gopakumar-vafa Invariantsmentioning

confidence: 59%