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arXiv · 1704.01050

Categorical Pl\"ucker Formula and Homological Projective Duality

Qingyuan Jiang·Naichung Conan Leung·Ying Xie
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Abstract

Homological Projective duality (HP-duality) theory, introduced by Kuznetsov [42], 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.

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Qingyuan Jiang, Naichung Conan Leung, Ying Xie. 2017-04-04. Categorical Pl\"ucker Formula and Homological Projective Duality. https://arxiv.org/abs/1704.01050

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