Geodesic
Homological projective duality
Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 157-220

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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 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.

@article{PMIHES_2007__105__157_0,
     author = {Kuznetsov, Alexander},
     title = {Homological projective duality},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {157--220},
     publisher = {Springer},
     volume = {105},
     year = {2007},
     doi = {10.1007/s10240-007-0006-8},
     mrnumber = {2354207},
     zbl = {1131.14017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-007-0006-8/}
}
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Kuznetsov, Alexander. Homological projective duality. Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 157-220. doi: 10.1007/s10240-007-0006-8

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