| Abstract |
This thesis studies varieties which admit a holomorphic symplectic form. We compute the LLV algebras of such varieties in terms of their Beauville-Bogomolov covering. Under some assumptions on the structure of the LLV algebras, we prove Orlov's conjecture for such varieties. This conjecture states that for two smooth projective complex varieties with equivalent derived categories there exists an isomorphism between their cohomology which preserves the grading and Hodge structure. This proof generalizes work by Taelman, who proved Orlov's conjecture for hyperkähler varieties.
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