4 problems

Let $V_d^{\operatorname{irr}}(S_1,\dots,S_r)$ denote the family of reduced irreducible complex plane curves of degree $d$ with isolated singular points of prescribed topological ty…

Let $S$ be a topological singularity type, let $r,d$ be positive integers, let $V_d^{\mathrm{irr}}(r\cdot S)$ denote the family of irreducible degree-$d$ plane curves with $r$ sing…

Let $H$ be a unisingular projective hypersurface, and let $H'$ vary along its equianalytic family. Write $Z^{ea}(H')$ for the equianalytic singularity scheme and let…

A family of hypersurface singularities is minimally obstructed when its equianalytic stratum has the minimal obstruction described in the preceding results. A hypersurface singular…