Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 118 / 5 / c

The Hodge decomposition theorem for compact Kähler manifolds gives a unique harmonic differential form representative of every complex de Rham cohomology class, with a decomposition into harmonic pure-type components. ConsequentlyEquivalently, the Dolbeault Hodge decomposition on a compact Hermitian manifold is