Stringy $E$-functions of Pfaffian�Grassmannian double mirrors

Libgober, Anatoly

doi:10.14231/ag-2019-022

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2021

2022

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Cited by 2 publications

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“…It would be interesting to try and extend the results of this paper to generalized Pfaffian varieties (cf. [30,Conjecture 6] and [56,Section 5.3] and [48] for the conjectural HPD statement, and [13] for a relation on the level of Hodge numbers).…”

Section: Introductionmentioning

confidence: 99%

Motives and the Pfaffian–Grassmannian equivalence

Laterveer

2021

J. London Math. Soc.

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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.

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Section: Introductionmentioning

confidence: 99%