Séminaire Lotharingien de Combinatoire, 89B.63 (2023), 12 pp.
Eugene Gorsky, Mikhail Mazin and Alexei Oblomkov
Generic Curves and Non-Coprime Catalans
Abstract.
We compute the Poincaré 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.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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