Homological projective duality

Kuznetsov, Alexander

doi:10.1007/s10240-007-0006-8

2007-07-20

124

Kuznetsov, Alexander *

DOI：10.1007/s10240-007-0006-8

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摘要

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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 serniorthogonal 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.