HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Abstract

Hilbert scheme topological invariants of plane curve singularities are identified to framed threefold stable pair invariants. As a result, the conjecture of Oblomkov and Shende on HOMFLY polynomials of links of plane curve singularities is given a Calabi-Yau threefold interpretation. The motivic Donaldson-Thomas theory developed by M. Kontsevich and the third author then yields natural motivic invariants for algebraic knots. This construction is motivated by previous work of V. Shende, C. Vafa and the first author on the large $N$ duality derivation of the above conjecture.

59 pages; v2 references added, minor corrections; v3: exposition improved, proofs expanded, results unchanged, to appear in Comm. Num. Th. Phys

References in corpus (6)

• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• Proofs of the integral identity conjecture over algebraically closed fields
• Generating functions of stable pair invariants via wall-crossings in derived categories
• Crepant resolutions and brane tilings II: Tilting bundles
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Macdonald formula for curves with planar singularities

Cited by in corpus (2)

• Legendrian knots and constructible sheaves
• Flops and Hilbert schemes of space curve singularities