Hodge structure
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. A polarized Hodge structure of weight "n" consists of a Hodge structure formula_17 and a non-degenerate integer bilinear form "Q" on formula_1 (polarization), which is extended to "H" by linearity, and satisfying the conditions: