The symplectic isotopy problem for rational cuspidal curves

We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. study the corresponding isotopy problem, with focus rational irreducible (rational cuspidal curves) projective plane. prove that every such is isotopic to degrees up five, and for one singularity link torus knot. Classification results classes rely pseudo-holomorphic together version birational geometry log pairs techniques from four-dimensional topology.