Complex manifolds. Kahler manifolds. Sheaves
2. Hodge decomposition
Elliptic operators and cohomology. Hodge and Lefschetz decomposition.
3. Spectral sequences
Filtered complexes and associated spectral sequences. The spectral sequence
associated with a double complex. Applications.
4. De Rham cohomology of complex manifolds
Hypercohomology. Holomorphic de Rham complex. Applications
to Hodge theory.
C. Voisin, Theorie de Hodge et geometrie algebrique
complexe, Societe' mathematique de France 2002
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