  We study lagrangian submanifolds of algebraic variety Gr(1, n) equipped with
the Kahler form given by the Plucker embedding. We use the correspondence
between lagrangian submanifolds of Gr(1, n) and lagrangian submanifolds of
variety M_{n-k}, given by symplectic reduction Gr(1, n)//T^k for some specially
chosen moment maps, which generate T^k action on Gr(1, n). We establish that in
this way one finds many topological types, realized by lagrangian submanifolds,
and then one counts that Gr(1, n) admits more than n different topological
types of smooth lagrangian submanifolds.
