Abstract
This chapter showcases two further lectures on the Hodge theory of maps, and they are mostly composed of exercises. The first lecture details a minimalist approach to sheaf cohomology, and then turns to the intersection cohomology complex, which is limited to the definition and calculation of the intersection complex Isubscript X of a variety of dimension d with one isolated singularity. Finally, this lecture discusses the Verdier duality. The second lecture sets out the Decomposition theorem, which is the deepest known fact concerning the homology of algebraic varieties. It then considers the relative hard Lefschetz and the hard Lefschetz for intersection cohomology groups.
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