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Kuznetsov’s homological projective duality (HPD) theory [K4] is one of the most active and powerful recent developments in the homological study of algebraic geometry. The fundamental theorem of HPD systematically compares derived categories of dual linear sections of a pair of HP-dual varieties .In this paper we generalize the fundamental theorem of HPD beyond linear sections. More precisely, we show that for any two pairs of HP-duals and which intersect properly, there exist semiorthogonal decompositions of the derived categories and into primitive and ambient parts, and that there is an equivalence of primitive parts .
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Qingyuan Jiang, Naichung Conan Leung, Ying Xie, Categorical Plücker Formula and Homological Projective Duality. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 1859–1898DOI 10.4171/JEMS/1045