Geodesic
DAHA and plane curve singularities
Cherednik, Ivan1 ; Philipp, Ian1
1 Mathematics Department, University of North Carolina, Chapel Hill, NC, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 333-385

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We suggest a relatively simple and totally geometric conjectural description of uncolored daha superpolynomials of arbitrary algebraic knots (conjecturally coinciding with the reduced stable Khovanov–Rozansky polynomials) via the flagged Jacobian factors (new objects) of the corresponding unibranch plane curve singularities. This generalizes the Cherednik–Danilenko conjecture on the Betti numbers of Jacobian factors, the Gorsky combinatorial conjectural interpretation of superpolynomials of torus knots and that by Gorsky and Mazin for their constant term. The paper mainly focuses on nontorus algebraic knots. A connection with the conjecture due to Oblomkov, Rasmussen and Shende is possible, but our approach is different. A  motivic version of our conjecture is related to p–adic orbital A–type integrals for anisotropic centralizers.

DOI : 10.2140/agt.2018.18.333
Classification : 14H50, 17B45, 20C08, 20F36, 33D52, 57M25, 17B22, 22E50, 22E57, 30F10, 33D80
Keywords: Hecke algebra, Jones polynomial, HOMFLYPT polynomial, Khovanov-Rozansky homology, algebraic knot, Macdonald polynomial, plane curve singularity, compactified Jacobian, Puiseux expansion, orbital integral

Cherednik, Ivan 1 ; Philipp, Ian 1

1 Mathematics Department, University of North Carolina, Chapel Hill, NC, United States 
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Cherednik, Ivan; Philipp, Ian. DAHA and plane curve singularities. Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 333-385. doi: 10.2140/agt.2018.18.333

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