# Homological projective duality

Publications Mathématiques de l'IHÉS (2007)

- Volume: 105, page 157-220
- ISSN: 0073-8301

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topKuznetsov, Alexander. "Homological projective duality." Publications Mathématiques de l'IHÉS 105 (2007): 157-220. <http://eudml.org/doc/104222>.

@article{Kuznetsov2007,

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.},

author = {Kuznetsov, Alexander},

journal = {Publications Mathématiques de l'IHÉS},

keywords = {projective duality; hyperplane sections; derived categories of singularities},

language = {eng},

pages = {157-220},

publisher = {Springer},

title = {Homological projective duality},

url = {http://eudml.org/doc/104222},

volume = {105},

year = {2007},

}

TY - JOUR

AU - Kuznetsov, Alexander

TI - Homological projective duality

JO - Publications Mathématiques de l'IHÉS

PY - 2007

PB - Springer

VL - 105

SP - 157

EP - 220

AB - 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.

LA - eng

KW - projective duality; hyperplane sections; derived categories of singularities

UR - http://eudml.org/doc/104222

ER -

## References

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