Compactified Jacobians and q,t-Catalan Numbers, I

Abstract

J. Piontkowski described the homology of the Jacobi factor of a plane curve singularity with one Puiseux pair. We discuss the combinatorial structure of his answer, in particular, relate it to the bigraded deformation of Catalan numbers introduced by A. Garsia and M. Haiman.

Revised version, 24 pages

References in corpus (10)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Stable pairs and BPS invariants
• BPS States, String Duality, and Nodal Curves on K3
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Euler number of the compactified Jacobian and multiplicity of rational curves
• Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation
• Affine Springer fibers of type A and combinatorics of diagonal coinvariants
• q,t-Catalan numbers and knot homology
• Macdonald formula for curves with planar singularities
• Combinatorics of certain higher $q,t$-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula

Cited by in corpus (5)

• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Rational parking functions and Catalan numbers
• Affine Springer fibers of type A and combinatorics of diagonal coinvariants
• Modules over plane curve singularities in any ranks and DAHA
• Duality and syzygies for semimodules over numerical semigroups