Homological projective duality |
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Authors: | Alexander Kuznetsov |
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Institution: | (1) Algebra Section, Steklov Mathematical Institute, 8 Gubkin str., Moscow, 119991, Russia |
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Abstract: | We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological
extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically
projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an
equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections
are equivalent. We also investigate homological projective duality for projectivizations of vector bundles. |
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