 On the other hand, the Hodge–de Rham spectral sequence supplies "Hn" with the decreasing filtration by "FpH" as in the second definition.For applications in algebraic geometry, namely, classification of complex projective varieties by their periods, the set of all Hodge structures of weight "n" on formula_1 is too big.Using the Riemann bilinear relations, in this case called "Hodge Riemann bilinear relations", it can be substantially simplified.