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 analyti cation 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).