  In this work we extend the residue theory from flag of holomorphic foliations
to flag of holomorphic distributions and we provide an effective way to
calculate this class in certain cases. As a consequence, we show that if we
consider a flag $\mathcal{F} = (\mathcal{F}_{1}, \mathcal{F}_{2})$ of
holomorphic distributions on $\mathbb{P}^{3}$, we get a relation between the
degrees of the distributions in the flag, the tangency order of distributions,
the Euler characteristic and the degree of the curve $C.$

Algebraic Geometry;Algebraic Topology;Complex Variables;Differential Geometry