Motives and the Pfaffian-Grassmannian equivalence
arXiv:2105.03171 · doi:10.1112/jlms.12473
Abstract
We consider the Pfaffian-Grassmannian equivalence from the motivic point of view. The main result is that under certain numerical conditions, both sides of the equivalence are related on the level of Chow motives. The consequences include a verification of Orlov's conjecture for Borisov's Calabi-Yau threefolds, and verifications of Kimura's finite-dimensionality conjecture, Voevodsky's smash conjecture and the Hodge conjecture for certain linear sections of Grassmannians. We also obtain new examples of Fano varieties with infinite-dimensional Griffiths group.
arXiv comment29 pages, to appear in Journal of the LMS, comments very welcome
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