Categorical Pl\"ucker Formula and Homological Projective Duality

JIANG Qingyuan The Chinese University of Hong Kong Naichung Conan LEUNG The Chinese University of Hong Kong XIE Ying The Chinese University of Hong Kong

Algebraic Geometry mathscidoc:1704.01002

Homological Projective duality (HP-duality) theory, introduced by Kuznetsov \cite{Kuz07HPD}, is one of the most powerful frameworks in the homological study of algebraic geometry. The main result (HP-duality theorem) of the theory gives complete descriptions of bounded derived categories of coherent sheaves of (dual) linear sections of HP-dual varieties. We show the theorem also holds for more general intersections beyond linear sections. More explicitly, for a given HP-dual pair $(X,Y)$, then analogue of HP-duality theorem holds for their intersections with another HP-dual pair $(S,T)$, provided that they intersect properly. We also prove a relative version of our main result. Taking $(S,T)$ to be dual linear subspaces (resp. subbundles), our method provides a more direct proof of the original (relative) HP-duality theorem.
Derived category of coherent sheaves, Homological Projective Duality, Pl\"ucker Formula, categorification, semiorthogonal decomposition, Lagrangian intersections,
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  • 68 pages, 5 figures.
@inproceedings{jiangcategorical,
  title={Categorical Pl\"ucker Formula and Homological Projective Duality},
  author={JIANG Qingyuan, Naichung Conan LEUNG, and XIE Ying},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170414135449267158740},
}
JIANG Qingyuan, Naichung Conan LEUNG, and XIE Ying. Categorical Pl\"ucker Formula and Homological Projective Duality. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170414135449267158740.
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