Invariant surfaces for toric type foliations in dimension three

A foliation is of toric type when it has a combinatorial reduction singularities. We show that every on (C3, 0) without saddle-nodes invariant surface. extend the argument Cano–Cerveau for nondicritical caseto compact dicritical components exceptional divisor. These are projective surfaces and isolated branches induced to closed irreducible curves. build surface as germ along singular locus those The result OrtizBobadilla–Rosales-Gonzalez–Voronin about distribution indimension two key in our proof.