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We continue the study of the rational-slope generalized $q,t$-Catalan numbers$c_{m,n}(q,t)$. We describe generalizations of the bijective constructions ofJ. Haglund and N. Loehr and use them to prove a weak symmetry property$c_{m,n}(q,1)=c_{m,n}(1,q)$ for $m=kn\pm 1$. We give a bijective proof of thefull symmetry $c_{m,n}(q,t)=c_{m,n}(t,q)$ for $\min(m,n)\le 3$. As a corollaryof these combinatorial constructions, we give a simple formula for thePoincar\'e polynomials of compactified Jacobians of plane curve singularities$x^{kn\pm 1}=y^n$. We also give a geometric interpretation of a relationbetween rational-slope Catalan numbers and the theory of $(m,n)$-coresdiscovered by J. Anderson.

Compactified Jacobians and q,t-Catalan numbers, II