Communications in Number Theory and Physics

Volume 6 (2012)

Number 3

HOMFLY polynomials, stable pairs and motivic Donaldson–Thomas invariants

Pages: 517 – 600

DOI: http://dx.doi.org/10.4310/CNTP.2012.v6.n3.a1

Authors

Duiliu-Emanuel Diaconescu (NHETC, Rutgers University, Piscataway, New Jersey, U.S.A.)

Zheng Hua (Department of Mathematics, Kansas State University, Manhattan, Ks., U.S.A.)

Yan Soibelman (Department of Mathematics, Kansas State University, Manhattan, Ks., U.S.A.)

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.

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