  In this work we study some problems related with algebraic hypersurfaces
invariant by foliations on weighted projective spaces
$\mathbb{P}_{\mathbb{C}}(\varpi_0,...,\varpi_n)$ generalizing some results
known for $\p$, as for example: the number of singularities, with
multiplicities, contained in the invariant quasi-smooth hypersurfaces; Poincare
problem on weighted projective plane and the number of the hypersurfaces, of a
degree fixed, invariant by a foliation on
$\mathbb{P}_{\mathbb{C}}(\varpi_0,...,\varpi_n)$ which does not admit a
rational first integral.
