The Hilbert scheme of a plane curve singularity and the \textsc{HOMFLY} homology of its link

DOI10.2140/gt.2018.22.645zbMath1388.14087arXiv1201.2115OpenAlexW3123082275MaRDI QIDQ680292

Jacob Rasmussen, Vivek Shende, Alexei Oblomkov

Publication date: 23 January 2018

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.2115

zbMATH Keywords

Hilbert schemeplane curveKhovanov homology

Mathematics Subject Classification ID

Related Items (33)

Towards \(\mathcal{R}\)-matrix construction of Khovanov-Rozansky polynomials I. Primary \(T\)-deformation of HOMFLY ⋮ Categorified Young symmetrizers and stable homology of torus links. II ⋮ Stable pairs and the HOMFLY polynomial ⋮ Modules over plane curve singularities in any ranks and DAHA ⋮ Introduction to Khovanov homologies. I. Unreduced Jones superpolynomial ⋮ Homology of torus knots ⋮ Superpolynomials for torus knots from evolution induced by cut-and-join operators ⋮ String theory and math: Why this marriage may last. Mathematics and dualities of quantum physics ⋮ Categorified Young symmetrizers and stable homology of torus links ⋮ The condensate from torus knots ⋮ Interplay between Macdonald and Hall-Littlewood expansions of extended torus superpolynomials ⋮ Knot homology and sheaves on the Hilbert scheme of points on the plane ⋮ HOMFLY-PT homology of Coxeter links ⋮ Algebra and geometry of link homology: Lecture notes from the IHES 2021 Summer School ⋮ Categorical Chern character and braid groups ⋮ Categorification: tangle invariants and TQFTs ⋮ Twisted spectral correspondence and torus knots ⋮ Compactified Jacobians and \(q,t\)-Catalan numbers. II ⋮ Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology ⋮ Constructing links of isolated singularities of polynomials ℝ4 → ℝ2 ⋮ A polynomial action on colored \(\mathfrak {sl}_2\) link homology ⋮ Refined knot invariants and Hilbert schemes ⋮ Legendrian knots and constructible sheaves ⋮ Exceptional knot homology ⋮ Serre duality for Khovanov-Rozansky homology ⋮ HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations ⋮ Orientifolds and the refined topological string ⋮ Tangle addition and the knots‐quivers correspondence ⋮ A support theorem for Hilbert schemes of planar curves, II ⋮ Gröbner cells of punctual Hilbert schemes in dimension two ⋮ The action of full twist on the superpolynomial for torus knots ⋮ A note on the E-polynomials of a stratification of the Hilbert scheme of points ⋮ Representations of rational Cherednik algebras with minimal support and torus knots.

Cites Work

• Unnamed Item
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• Unnamed Item
• A support theorem for Hilbert schemes of planar curves
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Torus knots and the rational DAHA
• Refined knot invariants and Hilbert schemes
• Global Springer theory
• Macdonald formula for curves with planar singularities
• Some differentials on Khovanov-Rozansky homology
• Matrix factorizations and link homology. II.
• The fundamental lemma for Lie algebras
• A continuous family of partition statistics equidistributed with length
• Finite-dimensional representations of DAHA and affine Springer fibers: the spherical case.
• Generalized divisors on Gorenstein curves and a theorem of Noether
• Compactifying the Picard scheme
• Conjectures on the quotient ring by diagonal invariants
• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Cherednik algebras and differential operators on quasi-invariants.
• On the category \(\mathcal O\) for rational Cherednik algebras.
• Compactified Jacobians and \(q,t\)-Catalan numbers. I.
• Conjectured statistics for the higher \(q,t\)-Catalan sequences
• Conjectured statistics for the \(q,t\)-Catalan numbers.
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• Parabolic induction and restriction functors for rational Cherednik algebras.
• Categorified Young symmetrizers and stable homology of torus links. II
• Homological thickness and stability of torus knots
• Topology of the compactified Jacobians of singular curves
• Rational Cherednik algebras and Hilbert schemes. II: Representations and sheaves
• Théorie de Hodge. II. (Hodge theory. II)
• Théorie de Hodge. III
• Rational Cherednik algebras and Hilbert schemes
• Symmetric products of an algebraic curve
• 𝑞,𝑡-Catalan numbers and knot homology
• Jones Polynomials of Torus Knots via DAHA
• Stable pairs and BPS invariants
• Meridian twisting of closed braids and the Homfly polynomial
• Morita equivalence of Cherednik algebras
• Universal KZB Equations: The Elliptic Case
• TRIPLY-GRADED LINK HOMOLOGY AND HOCHSCHILD HOMOLOGY OF SOERGEL BIMODULES
• Singular Points of Complex Hypersurfaces. (AM-61)
• Geometric representations of graded and rational Cherednik algebras

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