Homological Projective Duality

Details Homological Projective Duality Homological Projective Duality

2005-07-14

arxiv.org/abs/math/0507292v1

Mathematics

Algebraic Geometry

43 pages

Scientific paper

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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