Since , the line bundles on CP"n" are classified up to isomorphism by their Chern classes, which are integers: they lie in . In fact, the first Chern classes of complex projective space are generated under Poincaré duality by the homology class associated to a hyperplane "H". The line bundle "O"("kH") has Chern class "k". Hence every holomorphic line bundle on CP"n" is a tensor power of "O"("H") or "O"(−"H"). In other words, the Picard group of CP"n" is generated as an abelian group by the hyperplane class ["H"] .