  We study possible configurations of singular points occuring on general
algebraic curves in $\mathbb{C}P^2$ via Floer theory. To achieve this, we
describe a general formula for the $H_{1}$-action on the knot Floer complex of
the knotification of a link in $S^3$, in terms of natural actions on the link
Floer complex of the original link. This result may be interest on its own.
