Hodge Theory
Prof. Ugo Bruzzo
- Preliminaries
Complex manifolds. Kahler manifolds. Sheaves (reminder). - Hodge decomposition
Elliptic operators and cohomology. Hodge and Lefschetz decomposition. Hodge structures. - Spectral sequences
Filtered complexes and associated spectral sequences. The spectral sequence associated with a double complex. Applications. - 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