HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

Details HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants

2012-02-21

arxiv.org/abs/1202.4651v2

Mathematics

Algebraic Geometry

43 pages; v2 references added, minor corrections

Scientific paper

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.

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