Abstract
Homological Projective duality (HPduality) theory, introduced by Kuznetsov [42], is one of the most powerful frameworks in the homological study of algebraic geometry. The main result (HPduality theorem) of the theory gives complete descriptions of bounded derived categories of coherent sheaves of (dual) linear sections of HPdual varieties. We show the theorem also holds for more general intersections beyond linear sections. More explicitly, for a given HPdual pair (X,Y), then analogue of HPduality theorem holds for their intersections with another HPdual 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) HPduality theorem.
Original language  English 

Publisher  ArXiv 
Number of pages  68 
Publication status  Published  4 Apr 2017 
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Qingyuan Jiang
 School of Mathematics  Postdoctoral Research Associate
Person: Academic: Research Active