HODGE THEORY

Abstract

The main aim of this Thesis is to let the reader know about the connection between the theory of complex projective algebraic varieties and K¨ahler manifolds. A result by K¨odaira (which uses Hodge Decomposition) is that K¨ahler manifolds whose K¨ahler form are of integral cohomology class (called Polarised manifolds) are projective and the analytification of every smooth complex projective variety is a polarised manifold. There is also an introductory background in Spectral Sequences present in the thesis that is used to generalize Hodge Decomposition as degeneration of Fr¨olicher Spectral Sequence at E1; (i.e. page 1 of the spectral sequence).