Hodge Theory

Prof. Ugo Bruzzo

  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