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 (4)

• 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
• 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 (4)

• 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