Categorical duality between joins and intersections
Q Jiang, NC Leung - arXiv preprint arXiv:1811.05135, 2018 - arxiv.org
Q Jiang, NC Leung
arXiv preprint arXiv:1811.05135, 2018•arxiv.orgClassically, the projective duality between joins of varieties and the intersections of varieties
only holds in good cases. In this paper, we show that categorically, the duality between joins
and intersections holds in the framework of homological projective duality (HPD)[K07], as
long as the intersections have expected dimensions. This result together with its various
applications provide further evidences for the proposal of homological projective geometry
of Kuznetsov and Perry [KP18]. When the varieties are inside disjoint linear subspaces, our …
only holds in good cases. In this paper, we show that categorically, the duality between joins
and intersections holds in the framework of homological projective duality (HPD)[K07], as
long as the intersections have expected dimensions. This result together with its various
applications provide further evidences for the proposal of homological projective geometry
of Kuznetsov and Perry [KP18]. When the varieties are inside disjoint linear subspaces, our …
Classically, the projective duality between joins of varieties and the intersections of varieties only holds in good cases. In this paper, we show that categorically, the duality between joins and intersections holds in the framework of homological projective duality (HPD) [K07], as long as the intersections have expected dimensions. This result together with its various applications provide further evidences for the proposal of homological projective geometry of Kuznetsov and Perry [KP18]. When the varieties are inside disjoint linear subspaces, our approach also provides a new proof of the main result "formation of categorical joins commutes with HPD" of [KP18]. We also introduce the concept of an -HPD category, and study its properties and connections with joins and HPDs.
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