and Hodge Theory
Luca Migliorini (UniversitÓ di Bologna)
The aim of the course is to illustrate
some applications of the theory of perverse sheaves to Hodge theory and in particular
to the study of algebraic cycles. I will recall some fundamental results
about the category of perverse sheaves, emphasizing their connection to
classical results of Hodge theory such as the local invariant cycle theorem
and its generalization. Then I will discuss some recent results and
conjectures in this circle of ideas, namely:
The Hodge theoretic nature of the Leray
filtration (D. Arapura) and of the perverse Leray filtration (M. de Cataldo-L.
2. Green-Griffiths theory of normal
functions in several variables (M. Green-P. Griffiths, P. Brosnan-G.
Pearlstein, C. Schnell).
The projectors associated to the decomposition theorem for a
projective map are motivated cycles in the sense of Y. AndreÚ
(M. de Cataldo-L. M.).