  We study singularities of algebraic curves associated with 3d N=2 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
Poincare 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 N=2 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.
