"The Theory and Applications of Harmonic Integrals" summed up Hodge's development during the 1930s of his general theory. This starts with the existence for any Kähler metric of a theory of Laplacians – it applies to an algebraic variety "V" (assumed complex, projective and non-singular) because projective space itself carries such a metric. In de Rham cohomology terms, a cohomology class of degree "k" is represented by a "k"-form "α" on "V"(C). There is no unique representative; but by introducing the idea of "harmonic form" (Hodge still called them 'integrals'), which are solutions of Laplace's equation, one can get unique "α". This has the important, immediate consequence of splitting up