In a joint project with Eugene Gorsky and Alexei Oblomkov (arXiv:2210.12569) we study the Compactified Jacobians of the plane curve singularities given by a parametrization (x=t^dm, y=t^dn(1+Lt+...), where L is not zero. Here n and m are relatively prime, and d is greater than one. We show that the Compactified Jacobians in this case admit pavings by affine cells, enumerated by rational Dyck paths in a (dm x dn) rectangle. The Poincare polynomial of the Compactified Jacobian is then equal to a specialization of the corresponding rational (q,t)-Catalan polynomial. This generalizes the well known theory of Compactified Jacobians in the d=1 case.
Generic curves and non-coprime Catalans
08.11.2022 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: