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.
Categories: math.GT math.AG