Cazzador, Elisa (2017) Perverse sheaves and decomposition theorem. [Magistrali biennali]
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We introduce the notions of derived categories and t-structures. We study the theory of perverse sheaves and show that perverse objects form an abelian category. Combining topological aspects with a Hodge-theoretic point of view, we give a detailed proof of the Decomposition Theorem for semi-small proper algebraic maps whose domain is a smooth complex projective variety. Following the approach of De Cataldo and Migliorini, we proceed inductively on the strata of the target space and show that such decomposition is equivalent to the non-degeneracy of certain forms.
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