Hodge Theory
Ugo Bruzzo
CONTENTS
1. Preliminaries
Complex manifolds. Kahler manifolds. Sheaves
(reminder).
2. Hodge decomposition
Elliptic operators and cohomology. Hodge and Lefschetz decomposition.
Hodge structures.
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.
Reference text:
C. Voisin, Theorie de Hodge et geometrie algebrique
complexe, Societe' mathematique de France 2002
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