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://www.numdam.org/articles/10.1007/s10240-007-0006-8/}
}
TY - JOUR AU - Kuznetsov, Alexander TI - Homological projective duality JO - Publications Mathématiques de l'IHÉS PY - 2007 SP - 157 EP - 220 VL - 105 PB - Springer UR - http://www.numdam.org/articles/10.1007/s10240-007-0006-8/ DO - 10.1007/s10240-007-0006-8 LA - en ID - PMIHES_2007__105__157_0 ER -
Kuznetsov, Alexander. Homological projective duality. Publications Mathématiques de l'IHÉS, Tome 105 (2007), pp. 157-220. doi : 10.1007/s10240-007-0006-8. http://www.numdam.org/articles/10.1007/s10240-007-0006-8/
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