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We study singularities of algebraic curves associated with 3d theories that have at least one global flavor symmetry. Of particular interest is a class of theories T K labeled by knots, whose partition functions package Poincaré polynomials of the S r-colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d theories T K and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in S r-colored HOMFLY homologies.