Categorical Plücker Formula and Homological Projective Duality

Autor: Naichung Conan Leung, Qingyuan Jiang, Ying Xie
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Jiang, Q, Leung, N C & Xie, Y 2021, ' Categorical Plücker Formula and Homological Projective Duality ', Journal of the European Mathematical Society, vol. 23, no. 6, pp. 1859-1898 . https://doi.org/10.4171/JEMS/1045
DOI: 10.4171/JEMS/1045
Popis: 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.
Databáze: OpenAIRE