Motives and the Pfaffian-Grassmannian equivalence

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.

29 pages, to appear in Journal of the LMS, comments very welcome

References in corpus (5)

• Homological projective duality for Grassmannians of lines
• Fano manifolds of Calabi-Yau type
• The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians
• The generalized Hodge and Bloch conjectures are equivalent for general complete intersections, II
• Stringy $E$-functions of Pfaffian-Grassmannian double mirrors

Cited by in corpus (1)

• Some new Fano varieties with a multiplicative Chow-Künneth decomposition