Generic curves and non-coprime Catalans
Abstract
We compute the Poincar\'e polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents (nd,md,md+1), and relate them to the combinatorics of q,t-Catalan numbers in the non-coprime case. We also confirm a conjecture of Cherednik and Danilenko for such curves.
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