HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
Algebraic Geometry
2012-11-13 v3 High Energy Physics - Theory
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 duality derivation of the above conjecture.
Keywords
Cite
@article{arxiv.1202.4651,
title = {HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants},
author = {D. -E. Diaconescu and Z. Hua and Y. Soibelman},
journal= {arXiv preprint arXiv:1202.4651},
year = {2012}
}
Comments
59 pages; v2 references added, minor corrections; v3: exposition improved, proofs expanded, results unchanged, to appear in Comm. Num. Th. Phys