Nonlinearizable CR Automorphisms for Polynomial Models in $$\mathbb C^N$$

The Lie algebra of infinitesimal CR automorphisms is a fundamental local invariant manifold. Motivated by the Poincaré equivalence problem, we analyze its positively graded components, containing nonlinearizable holomorphic vector fields. results provide complete description weighted homogeneous polynomial models in $$\mathbb C^N$$ , which admit symmetries degree higher than two. For models, with quadratic coefficients are also classified completely. As consequence, this provides an optimal 1-jet determination result general case. Further prove that such arise from one common source, pulling back via mapping suitable symmetry hyperquadric some (typically high dimensional) complex space.