JournalsjemsVol. 23, No. 6pp. 1859–1898

Categorical Plücker Formula and Homological Projective Duality

  • Qingyuan Jiang

    Institute for Advanced Study, Princeton, USA and University of Edinburgh, UK
  • Naichung Conan Leung

    The Chinese University of Hong Kong, Hong Kong
  • Ying Xie

    The Chinese University of Hong Kong, Hong Kong
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Abstract

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 (X,X)(X,X^{\natural}).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 (X,X)(X,X^{\natural}) and (T,T)(T,T^{\natural}) which intersect properly, there exist semiorthogonal decompositions of the derived categories D(XT)D(X \cap T) and D(XT)D(X^{\natural} \cap T^{\natural}) into primitive and ambient parts, and that there is an equivalence of primitive parts primD(XT)D(XT)prim^\mathrm {prim} D(X \cap T) \simeq D(X^{\natural} \cap T^{\natural})^{\mathrm prim}.

Cite this article

Qingyuan Jiang, Naichung Conan Leung, Ying Xie, Categorical Plücker Formula and Homological Projective Duality. J. Eur. Math. Soc. 23 (2021), no. 6, pp. 1859–1898

DOI 10.4171/JEMS/1045