Topology of Generic Multijet Preimages and Blow-Up via Newton Interpolation

We study the local topological structure of generic multijet preimages of algebraic varieties and prove their stratifiability with additional quantitative estimates. The result is a necessary technical tool for analyzing bifurcations of periodic orbits from heteroclinic polygons of vector fields in space. The proof is based on interpretation of Newton interpolation formula as a resolution of singularities on the diagonal of the multijet space.