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arXiv · 2210.12569

Generic curves and non-coprime Catalans

Eugene Gorsky·Mikhail Mazin·Alexei Oblomkov
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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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Eugene Gorsky, Mikhail Mazin, Alexei Oblomkov. 2022-10-22. Generic curves and non-coprime Catalans. https://arxiv.org/abs/2210.12569

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