Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categorical Pl\"ucker Formula and Homological Projective Duality   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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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org